LMFDB - Embedded newform 208.2.n.a.157.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,2,Mod(53,208)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("208.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	208.n (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.66088836204$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			157.10
Character	$\chi$	$=$	208.157
Dual form			208.2.n.a.53.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.395977 + 1.35765i) q^{2} +(-0.140536 - 0.140536i) q^{3} +(-1.68640 - 1.07519i) q^{4} +(1.99922 - 1.99922i) q^{5} +(0.246447 - 0.135149i) q^{6} -0.679168i q^{7} +(2.12751 - 1.86379i) q^{8} -2.96050i q^{9} +O(q^{10})$	\(q+(-0.395977 + 1.35765i) q^{2} +(-0.140536 - 0.140536i) q^{3} +(-1.68640 - 1.07519i) q^{4} +(1.99922 - 1.99922i) q^{5} +(0.246447 - 0.135149i) q^{6} -0.679168i q^{7} +(2.12751 - 1.86379i) q^{8} -2.96050i q^{9} +(1.92259 + 3.50588i) q^{10} +(0.156646 - 0.156646i) q^{11} +(0.0858968 + 0.388103i) q^{12} +(0.707107 + 0.707107i) q^{13} +(0.922069 + 0.268935i) q^{14} -0.561924 q^{15} +(1.68792 + 3.62642i) q^{16} +3.23000 q^{17} +(4.01931 + 1.17229i) q^{18} +(-0.408747 - 0.408747i) q^{19} +(-5.52105 + 1.22195i) q^{20} +(-0.0954473 + 0.0954473i) q^{21} +(0.150642 + 0.274699i) q^{22} +6.63737i q^{23} +(-0.560919 - 0.0370625i) q^{24} -2.99379i q^{25} +(-1.24000 + 0.680002i) q^{26} +(-0.837663 + 0.837663i) q^{27} +(-0.730237 + 1.14535i) q^{28} +(-4.96165 - 4.96165i) q^{29} +(0.222509 - 0.762894i) q^{30} +2.26501 q^{31} +(-5.59177 + 0.855612i) q^{32} -0.0440288 q^{33} +(-1.27901 + 4.38519i) q^{34} +(-1.35781 - 1.35781i) q^{35} +(-3.18311 + 4.99260i) q^{36} +(2.37078 - 2.37078i) q^{37} +(0.716788 - 0.393079i) q^{38} -0.198747i q^{39} +(0.527242 - 7.97949i) q^{40} +5.79456i q^{41} +(-0.0917886 - 0.167379i) q^{42} +(4.85187 - 4.85187i) q^{43} +(-0.432594 + 0.0957439i) q^{44} +(-5.91870 - 5.91870i) q^{45} +(-9.01120 - 2.62825i) q^{46} -12.8753 q^{47} +(0.272429 - 0.746854i) q^{48} +6.53873 q^{49} +(4.06450 + 1.18547i) q^{50} +(-0.453930 - 0.453930i) q^{51} +(-0.432191 - 1.95274i) q^{52} +(-0.139449 + 0.139449i) q^{53} +(-0.805554 - 1.46894i) q^{54} -0.626342i q^{55} +(-1.26582 - 1.44494i) q^{56} +0.114887i q^{57} +(8.70087 - 4.77146i) q^{58} +(-0.930857 + 0.930857i) q^{59} +(0.947631 + 0.604177i) q^{60} +(-1.62312 - 1.62312i) q^{61} +(-0.896894 + 3.07509i) q^{62} -2.01068 q^{63} +(1.05260 - 7.93045i) q^{64} +2.82733 q^{65} +(0.0174344 - 0.0597755i) q^{66} +(4.82880 + 4.82880i) q^{67} +(-5.44708 - 3.47287i) q^{68} +(0.932787 - 0.932787i) q^{69} +(2.38108 - 1.30576i) q^{70} +15.4616i q^{71} +(-5.51774 - 6.29849i) q^{72} +9.54473i q^{73} +(2.27991 + 4.15746i) q^{74} +(-0.420734 + 0.420734i) q^{75} +(0.249830 + 1.12879i) q^{76} +(-0.106389 - 0.106389i) q^{77} +(0.269829 + 0.0786995i) q^{78} -14.4573 q^{79} +(10.6246 + 3.87551i) q^{80} -8.64606 q^{81} +(-7.86696 - 2.29452i) q^{82} +(4.28152 + 4.28152i) q^{83} +(0.263587 - 0.0583383i) q^{84} +(6.45749 - 6.45749i) q^{85} +(4.66589 + 8.50836i) q^{86} +1.39458i q^{87} +(0.0413113 - 0.625222i) q^{88} +11.7067i q^{89} +(10.3792 - 5.69183i) q^{90} +(0.480244 - 0.480244i) q^{91} +(7.13646 - 11.1933i) q^{92} +(-0.318315 - 0.318315i) q^{93} +(5.09833 - 17.4801i) q^{94} -1.63435 q^{95} +(0.906087 + 0.665599i) q^{96} +5.00115 q^{97} +(-2.58919 + 8.87728i) q^{98} +(-0.463752 - 0.463752i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4} - 12 q^{8}+O(q^{10}) $ 48 * q - 4 * q^4 - 12 * q^8	$ 48 q - 4 q^{4} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 8 q^{12} - 4 q^{14} - 16 q^{15} + 12 q^{16} - 16 q^{19} - 28 q^{20} + 12 q^{22} + 28 q^{24} - 16 q^{29} + 4 q^{30} + 24 q^{31} - 20 q^{32} - 40 q^{34} + 24 q^{35} + 8 q^{36} - 16 q^{37} + 32 q^{40} + 40 q^{42} - 8 q^{43} + 20 q^{44} - 32 q^{46} - 40 q^{47} - 52 q^{48} - 48 q^{49} - 16 q^{50} - 24 q^{51} - 8 q^{52} + 16 q^{53} + 20 q^{54} + 20 q^{56} - 16 q^{58} - 68 q^{60} + 32 q^{61} - 32 q^{62} + 40 q^{63} + 32 q^{64} - 32 q^{66} + 16 q^{67} + 40 q^{68} + 32 q^{69} - 60 q^{70} + 40 q^{72} + 72 q^{74} - 40 q^{75} - 28 q^{76} + 16 q^{77} + 32 q^{79} - 52 q^{80} - 48 q^{81} + 40 q^{82} + 40 q^{83} - 36 q^{84} - 32 q^{85} - 72 q^{86} - 8 q^{88} + 28 q^{90} + 36 q^{92} + 28 q^{94} - 48 q^{95} + 68 q^{96} + 64 q^{98} - 40 q^{99}+O(q^{100}) $ 48 * q - 4 * q^4 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 8 * q^12 - 4 * q^14 - 16 * q^15 + 12 * q^16 - 16 * q^19 - 28 * q^20 + 12 * q^22 + 28 * q^24 - 16 * q^29 + 4 * q^30 + 24 * q^31 - 20 * q^32 - 40 * q^34 + 24 * q^35 + 8 * q^36 - 16 * q^37 + 32 * q^40 + 40 * q^42 - 8 * q^43 + 20 * q^44 - 32 * q^46 - 40 * q^47 - 52 * q^48 - 48 * q^49 - 16 * q^50 - 24 * q^51 - 8 * q^52 + 16 * q^53 + 20 * q^54 + 20 * q^56 - 16 * q^58 - 68 * q^60 + 32 * q^61 - 32 * q^62 + 40 * q^63 + 32 * q^64 - 32 * q^66 + 16 * q^67 + 40 * q^68 + 32 * q^69 - 60 * q^70 + 40 * q^72 + 72 * q^74 - 40 * q^75 - 28 * q^76 + 16 * q^77 + 32 * q^79 - 52 * q^80 - 48 * q^81 + 40 * q^82 + 40 * q^83 - 36 * q^84 - 32 * q^85 - 72 * q^86 - 8 * q^88 + 28 * q^90 + 36 * q^92 + 28 * q^94 - 48 * q^95 + 68 * q^96 + 64 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.395977	+	1.35765i	−0.279998	+	0.960001i
$2$	−0.395977	+	1.35765i	−0.279998	+	0.960001i
$3$	−0.140536	−	0.140536i	−0.0811383	−	0.0811383i	0.665373	−	0.746511i	$-0.268273\pi$
$3$	−0.140536	−	0.140536i	−0.0811383	−	0.0811383i	−0.746511	+	0.665373i	$0.768273\pi$
$4$	−1.68640	−	1.07519i	−0.843202	−	0.537597i
$5$	1.99922	−	1.99922i	0.894080	−	0.894080i	−0.100824	−	0.994904i	$-0.532148\pi$
$5$	1.99922	−	1.99922i	0.894080	−	0.894080i	0.994904	+	0.100824i	$0.0321480\pi$
$6$	0.246447	−	0.135149i	0.100611	−	0.0551742i
$7$		−	0.679168i		−	0.256701i	−0.991729	−	0.128351i	$-0.959032\pi$
$7$		−	0.679168i		−	0.256701i	0.991729	−	0.128351i	$-0.0409683\pi$
$8$	2.12751	−	1.86379i	0.752188	−	0.658948i
$9$		−	2.96050i		−	0.986833i
$10$	1.92259	+	3.50588i	0.607976	+	1.10866i
$11$	0.156646	−	0.156646i	0.0472307	−	0.0472307i	−0.683097	−	0.730328i	$-0.739367\pi$
$11$	0.156646	−	0.156646i	0.0472307	−	0.0472307i	0.730328	+	0.683097i	$0.239367\pi$
$12$	0.0858968	+	0.388103i	0.0247963	+	0.112036i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$14$	0.922069	+	0.268935i	0.246433	+	0.0718759i
$15$	−0.561924			−0.145088
$16$	1.68792	+	3.62642i	0.421979	+	0.906606i
$17$	3.23000			0.783389			0.391695	−	0.920095i	$-0.371889\pi$
$17$	3.23000			0.783389			0.391695	+	0.920095i	$0.371889\pi$
$18$	4.01931	+	1.17229i	0.947360	+	0.276312i
$19$	−0.408747	−	0.408747i	−0.0937729	−	0.0937729i	0.658664	−	0.752437i	$-0.271122\pi$
$19$	−0.408747	−	0.408747i	−0.0937729	−	0.0937729i	−0.752437	+	0.658664i	$0.771122\pi$
$20$	−5.52105	+	1.22195i	−1.23454	+	0.273235i
$21$	−0.0954473	+	0.0954473i	−0.0208283	+	0.0208283i
$22$	0.150642	+	0.274699i	0.0321170	+	0.0585660i
$23$			6.63737i			1.38399i	0.721904	+	0.691994i	$0.243267\pi$
$23$			6.63737i			1.38399i	−0.721904	+	0.691994i	$0.756733\pi$
$24$	−0.560919	−	0.0370625i	−0.114497	−	0.00756536i
$25$		−	2.99379i		−	0.598758i
$26$	−1.24000	+	0.680002i	−0.243184	+	0.133359i
$27$	−0.837663	+	0.837663i	−0.161208	+	0.161208i
$28$	−0.730237	+	1.14535i	−0.138002	+	0.216451i
$29$	−4.96165	−	4.96165i	−0.921356	−	0.921356i	0.0757697	−	0.997125i	$-0.475859\pi$
$29$	−4.96165	−	4.96165i	−0.921356	−	0.921356i	−0.997125	+	0.0757697i	$0.975859\pi$
$30$	0.222509	−	0.762894i	0.0406244	−	0.139285i
$31$	2.26501			0.406809			0.203404	−	0.979095i	$-0.434799\pi$
$31$	2.26501			0.406809			0.203404	+	0.979095i	$0.434799\pi$
$32$	−5.59177	+	0.855612i	−0.988495	+	0.151252i
$33$	−0.0440288			−0.00766443
$34$	−1.27901	+	4.38519i	−0.219348	+	0.752054i
$35$	−1.35781	−	1.35781i	−0.229511	−	0.229511i
$36$	−3.18311	+	4.99260i	−0.530518	+	0.832100i
$37$	2.37078	−	2.37078i	0.389754	−	0.389754i	−0.484845	−	0.874600i	$-0.661124\pi$
$37$	2.37078	−	2.37078i	0.389754	−	0.389754i	0.874600	+	0.484845i	$0.161124\pi$
$38$	0.716788	−	0.393079i	0.116278	−	0.0637658i
$39$		−	0.198747i		−	0.0318251i
$40$	0.527242	−	7.97949i	0.0833643	−	1.26167i
$41$			5.79456i			0.904959i	0.891775	+	0.452479i	$0.149460\pi$
$41$			5.79456i			0.904959i	−0.891775	+	0.452479i	$0.850540\pi$
$42$	−0.0917886	−	0.167379i	−0.0141633	−	0.0258271i
$43$	4.85187	−	4.85187i	0.739904	−	0.739904i	−0.232656	−	0.972559i	$-0.574741\pi$
$43$	4.85187	−	4.85187i	0.739904	−	0.739904i	0.972559	+	0.232656i	$0.0747415\pi$
$44$	−0.432594	+	0.0957439i	−0.0652161	+	0.0144339i
$45$	−5.91870	−	5.91870i	−0.882308	−	0.882308i
$46$	−9.01120	−	2.62825i	−1.32863	−	0.387514i
$47$	−12.8753			−1.87806			−0.939028	−	0.343842i	$-0.888272\pi$
$47$	−12.8753			−1.87806			−0.939028	+	0.343842i	$0.888272\pi$
$48$	0.272429	−	0.746854i	0.0393218	−	0.107799i
$49$	6.53873			0.934104
$50$	4.06450	+	1.18547i	0.574808	+	0.167651i
$51$	−0.453930	−	0.453930i	−0.0635629	−	0.0635629i
$52$	−0.432191	−	1.95274i	−0.0599341	−	0.270797i
$53$	−0.139449	+	0.139449i	−0.0191548	+	0.0191548i	−0.716619	−	0.697465i	$-0.754311\pi$
$53$	−0.139449	+	0.139449i	−0.0191548	+	0.0191548i	0.697465	+	0.716619i	$0.254311\pi$
$54$	−0.805554	−	1.46894i	−0.109622	−	0.199898i
$55$		−	0.626342i		−	0.0844560i
$56$	−1.26582	−	1.44494i	−0.169153	−	0.193088i
$57$			0.114887i			0.0152171i
$58$	8.70087	−	4.77146i	1.14248	−	0.626524i
$59$	−0.930857	+	0.930857i	−0.121187	+	0.121187i	−0.765099	−	0.643912i	$-0.777310\pi$
$59$	−0.930857	+	0.930857i	−0.121187	+	0.121187i	0.643912	+	0.765099i	$0.277310\pi$
$60$	0.947631	+	0.604177i	0.122339	+	0.0779990i
$61$	−1.62312	−	1.62312i	−0.207819	−	0.207819i	0.595521	−	0.803340i	$-0.296946\pi$
$61$	−1.62312	−	1.62312i	−0.207819	−	0.207819i	−0.803340	+	0.595521i	$0.796946\pi$
$62$	−0.896894	+	3.07509i	−0.113906	+	0.390536i
$63$	−2.01068			−0.253321
$64$	1.05260	−	7.93045i	0.131575	−	0.991306i
$65$	2.82733			0.350687
$66$	0.0174344	−	0.0597755i	0.00214603	−	0.00735786i
$67$	4.82880	+	4.82880i	0.589932	+	0.589932i	0.937613	−	0.347681i	$-0.113031\pi$
$67$	4.82880	+	4.82880i	0.589932	+	0.589932i	−0.347681	+	0.937613i	$0.613031\pi$
$68$	−5.44708	−	3.47287i	−0.660556	−	0.421148i
$69$	0.932787	−	0.932787i	0.112294	−	0.112294i
$70$	2.38108	−	1.30576i	0.284594	−	0.156068i
$71$			15.4616i			1.83495i	0.397795	+	0.917474i	$0.369775\pi$
$71$			15.4616i			1.83495i	−0.397795	+	0.917474i	$0.630225\pi$
$72$	−5.51774	−	6.29849i	−0.650272	−	0.742284i
$73$			9.54473i			1.11713i	0.829462	+	0.558563i	$0.188647\pi$
$73$			9.54473i			1.11713i	−0.829462	+	0.558563i	$0.811353\pi$
$74$	2.27991	+	4.15746i	0.265034	+	0.483295i
$75$	−0.420734	+	0.420734i	−0.0485822	+	0.0485822i
$76$	0.249830	+	1.12879i	0.0286575	+	0.129482i
$77$	−0.106389	−	0.106389i	−0.0121242	−	0.0121242i
$78$	0.269829	+	0.0786995i	0.0305521	+	0.00891096i
$79$	−14.4573			−1.62658			−0.813289	−	0.581860i	$-0.802325\pi$
$79$	−14.4573			−1.62658			−0.813289	+	0.581860i	$0.802325\pi$
$80$	10.6246	+	3.87551i	1.18786	+	0.433295i
$81$	−8.64606			−0.960673
$82$	−7.86696	−	2.29452i	−0.868761	−	0.253387i
$83$	4.28152	+	4.28152i	0.469958	+	0.469958i	0.901901	−	0.431943i	$-0.142172\pi$
$83$	4.28152	+	4.28152i	0.469958	+	0.469958i	−0.431943	+	0.901901i	$0.642172\pi$
$84$	0.263587	−	0.0583383i	0.0287597	−	0.00636523i
$85$	6.45749	−	6.45749i	0.700413	−	0.700413i
$86$	4.66589	+	8.50836i	0.503136	+	0.917480i
$87$			1.39458i			0.149514i
$88$	0.0413113	−	0.625222i	0.00440380	−	0.0666489i
$89$			11.7067i			1.24090i	0.784245	+	0.620451i	$0.213051\pi$
$89$			11.7067i			1.24090i	−0.784245	+	0.620451i	$0.786949\pi$
$90$	10.3792	−	5.69183i	1.09406	−	0.599971i
$91$	0.480244	−	0.480244i	0.0503433	−	0.0503433i
$92$	7.13646	−	11.1933i	0.744027	−	1.16698i
$93$	−0.318315	−	0.318315i	−0.0330078	−	0.0330078i
$94$	5.09833	−	17.4801i	0.525852	−	1.80293i
$95$	−1.63435			−0.167681
$96$	0.906087	+	0.665599i	0.0924771	+	0.0679325i
$97$	5.00115			0.507790			0.253895	−	0.967232i	$-0.418288\pi$
$97$	5.00115			0.507790			0.253895	+	0.967232i	$0.418288\pi$
$98$	−2.58919	+	8.87728i	−0.261548	+	0.896741i
$99$	−0.463752	−	0.463752i	−0.0466088	−	0.0466088i
$100$	−3.21890	+	5.04874i	−0.321890	+	0.504874i
$101$	−6.20086	+	6.20086i	−0.617009	+	0.617009i	−0.944763	−	0.327754i	$-0.893708\pi$
$101$	−6.20086	+	6.20086i	−0.617009	+	0.617009i	0.327754	+	0.944763i	$0.393708\pi$
$102$	0.796022	−	0.436530i	0.0788179	−	0.0432229i
$103$		−	4.13967i		−	0.407894i	−0.978982	−	0.203947i	$-0.934623\pi$
$103$		−	4.13967i		−	0.407894i	0.978982	−	0.203947i	$-0.0653770\pi$
$104$	2.82227	+	0.186481i	0.276747	+	0.0182859i
$105$			0.381641i			0.0372443i
$106$	−0.134104	−	0.244541i	−0.0130253	−	0.0237520i
$107$	4.67646	−	4.67646i	0.452090	−	0.452090i	−0.443958	−	0.896048i	$-0.646426\pi$
$107$	4.67646	−	4.67646i	0.452090	−	0.452090i	0.896048	+	0.443958i	$0.146426\pi$
$108$	2.31329	−	0.511988i	0.222596	−	0.0492660i
$109$	−0.519710	−	0.519710i	−0.0497792	−	0.0497792i	0.681779	−	0.731558i	$-0.261207\pi$
$109$	−0.519710	−	0.519710i	−0.0497792	−	0.0497792i	−0.731558	+	0.681779i	$0.761207\pi$
$110$	0.850351	+	0.248017i	0.0810778	+	0.0236475i
$111$	−0.666359			−0.0632480
$112$	2.46295	−	1.14638i	0.232727	−	0.108323i
$113$	14.4614			1.36041			0.680207	−	0.733020i	$-0.261890\pi$
$113$	14.4614			1.36041			0.680207	+	0.733020i	$0.261890\pi$
$114$	−0.155976	−	0.0454926i	−0.0146085	−	0.00426077i
$115$	13.2696	+	13.2696i	1.23740	+	1.23740i
$116$	3.03261	+	13.7021i	0.281571	+	1.27221i
$117$	2.09339	−	2.09339i	0.193534	−	0.193534i
$118$	−0.895176	−	1.63237i	−0.0824076	−	0.150272i
$119$		−	2.19371i		−	0.201097i
$120$	−1.19550	+	1.04731i	−0.109134	+	0.0956056i
$121$			10.9509i			0.995539i
$122$	2.84633	−	1.56090i	0.257695	−	0.141317i
$123$	0.814342	−	0.814342i	0.0734268	−	0.0734268i
$124$	−3.81973	−	2.43533i	−0.343022	−	0.218699i
$125$	4.01086	+	4.01086i	0.358743	+	0.358743i
$126$	0.796182	−	2.72979i	0.0709295	−	0.243189i
$127$	17.5656			1.55870			0.779348	−	0.626591i	$-0.215550\pi$
$127$	17.5656			1.55870			0.779348	+	0.626591i	$0.215550\pi$
$128$	10.3499	+	4.56933i	0.914814	+	0.403876i
$129$	−1.36372			−0.120069
$130$	−1.11956	+	3.83851i	−0.0981917	+	0.336660i
$131$	−14.7833	−	14.7833i	−1.29162	−	1.29162i	−0.933783	−	0.357839i	$-0.883514\pi$
$131$	−14.7833	−	14.7833i	−1.29162	−	1.29162i	−0.357839	−	0.933783i	$-0.616486\pi$
$132$	0.0742503	+	0.0473395i	0.00646266	+	0.00412037i
$133$	−0.277608	+	0.277608i	−0.0240716	+	0.0240716i
$134$	−8.46790	+	4.64371i	−0.731515	+	0.401155i
$135$			3.34935i			0.288266i
$136$	6.87185	−	6.02003i	0.589256	−	0.516213i
$137$		−	7.69981i		−	0.657839i	−0.944358	−	0.328919i	$-0.893316\pi$
$137$		−	7.69981i		−	0.657839i	0.944358	−	0.328919i	$-0.106684\pi$
$138$	0.897032	+	1.63576i	0.0763604	+	0.139245i
$139$	11.1063	−	11.1063i	0.942023	−	0.942023i	−0.0563856	−	0.998409i	$-0.517958\pi$
$139$	11.1063	−	11.1063i	0.942023	−	0.942023i	0.998409	+	0.0563856i	$0.0179576\pi$
$140$	0.829906	+	3.74972i	0.0701399	+	0.316909i
$141$	1.80944	+	1.80944i	0.152382	+	0.152382i
$142$	−20.9913	−	6.12242i	−1.76155	−	0.513782i
$143$	0.221531			0.0185254
$144$	10.7360	−	4.99708i	0.894668	−	0.416423i
$145$	−19.8389			−1.64753
$146$	−12.9584	−	3.77950i	−1.07244	−	0.312793i
$147$	−0.918925	−	0.918925i	−0.0757916	−	0.0757916i
$148$	−6.54715	+	1.44905i	−0.538173	+	0.119111i
$149$	−14.9694	+	14.9694i	−1.22634	+	1.22634i	−0.261000	+	0.965339i	$0.584052\pi$
$149$	−14.9694	+	14.9694i	−1.22634	+	1.22634i	−0.965339	+	0.261000i	$0.915948\pi$
$150$	−0.404607	−	0.737809i	−0.0330360	−	0.0602418i
$151$		−	4.03152i		−	0.328080i	−0.986454	−	0.164040i	$-0.947547\pi$
$151$		−	4.03152i		−	0.328080i	0.986454	−	0.164040i	$-0.0524527\pi$
$152$	−1.63143	−	0.107796i	−0.132326	−	0.00874341i
$153$		−	9.56241i		−	0.773075i
$154$	0.186567	−	0.102311i	0.0150340	−	0.00824446i
$155$	4.52827	−	4.52827i	0.363719	−	0.363719i
$156$	−0.213692	+	0.335168i	−0.0171091	+	0.0268349i
$157$	−1.14652	−	1.14652i	−0.0915020	−	0.0915020i	0.659874	−	0.751376i	$-0.270610\pi$
$157$	−1.14652	−	1.14652i	−0.0915020	−	0.0915020i	−0.751376	+	0.659874i	$0.770610\pi$
$158$	5.72478	−	19.6279i	0.455439	−	1.56152i
$159$	0.0391952			0.00310838
$160$	−9.46865	+	12.8898i	−0.748562	+	1.01903i
$161$	4.50789			0.355271
$162$	3.42364	−	11.7383i	0.268987	−	0.922246i
$163$	−5.49430	−	5.49430i	−0.430346	−	0.430346i	0.458400	−	0.888746i	$-0.348423\pi$
$163$	−5.49430	−	5.49430i	−0.430346	−	0.430346i	−0.888746	+	0.458400i	$0.848423\pi$
$164$	6.23028	−	9.77197i	0.486503	−	0.763063i
$165$	−0.0880234	+	0.0880234i	−0.00685261	+	0.00685261i
$166$	−7.50817	+	4.11740i	−0.582747	+	0.319572i
$167$		−	4.03011i		−	0.311859i	−0.987768	−	0.155930i	$-0.950163\pi$
$167$		−	4.03011i		−	0.311859i	0.987768	−	0.155930i	$-0.0498373\pi$
$168$	−0.0251717	+	0.380958i	−0.00194204	+	0.0293916i
$169$			1.00000i			0.0769231i
$170$	6.20996	+	11.3240i	0.476282	+	0.868511i
$171$	−1.21009	+	1.21009i	−0.0925382	+	0.0925382i
$172$	−13.3989	+	2.96551i	−1.02166	+	0.226118i
$173$	−12.2652	−	12.2652i	−0.932507	−	0.932507i	0.0653552	−	0.997862i	$-0.479182\pi$
$173$	−12.2652	−	12.2652i	−0.932507	−	0.932507i	−0.997862	+	0.0653552i	$0.979182\pi$
$174$	−1.89334	−	0.552221i	−0.143534	−	0.0418638i
$175$	−2.03328			−0.153702
$176$	0.832472	+	0.303660i	0.0627499	+	0.0228892i
$177$	0.261637			0.0196659
$178$	−15.8935	−	4.63557i	−1.19127	−	0.347451i
$179$	−9.54466	−	9.54466i	−0.713401	−	0.713401i	0.253844	−	0.967245i	$-0.418305\pi$
$179$	−9.54466	−	9.54466i	−0.713401	−	0.713401i	−0.967245	+	0.253844i	$0.918305\pi$
$180$	3.61757	+	16.3451i	0.269638	+	1.21829i
$181$	−11.5003	+	11.5003i	−0.854808	+	0.854808i	−0.990721	−	0.135913i	$-0.956603\pi$
$181$	−11.5003	+	11.5003i	−0.854808	+	0.854808i	0.135913	+	0.990721i	$0.456603\pi$
$182$	0.461836	+	0.842167i	0.0342335	+	0.0624256i
$183$			0.456211i			0.0337241i
$184$	12.3706	+	14.1211i	0.911976	+	1.04102i
$185$		−	9.47945i		−	0.696943i
$186$	0.558205	−	0.306114i	0.0409296	−	0.0224453i
$187$	0.505967	−	0.505967i	0.0370000	−	0.0370000i
$188$	21.7130	+	13.8434i	1.58358	+	1.00964i
$189$	0.568913	+	0.568913i	0.0413824	+	0.0413824i
$190$	0.647166	−	2.21887i	0.0469504	−	0.160974i
$191$	12.9940			0.940213			0.470106	−	0.882610i	$-0.344216\pi$
$191$	12.9940			0.940213			0.470106	+	0.882610i	$0.344216\pi$
$192$	−1.26244	+	0.966583i	−0.0911086	+	0.0697571i
$193$	−11.8931			−0.856088			−0.428044	−	0.903758i	$-0.640797\pi$
$193$	−11.8931			−0.856088			−0.428044	+	0.903758i	$0.640797\pi$
$194$	−1.98034	+	6.78979i	−0.142180	+	0.487478i
$195$	−0.397340	−	0.397340i	−0.0284541	−	0.0284541i
$196$	−11.0269	−	7.03040i	−0.787639	−	0.502172i
$197$	−10.0235	+	10.0235i	−0.714147	+	0.714147i	−0.967400	−	0.253253i	$-0.918499\pi$
$197$	−10.0235	+	10.0235i	−0.714147	+	0.714147i	0.253253	+	0.967400i	$0.418499\pi$
$198$	0.813245	−	0.445975i	0.0577948	−	0.0316941i
$199$		−	8.65351i		−	0.613431i	−0.951801	−	0.306715i	$-0.900770\pi$
$199$		−	8.65351i		−	0.613431i	0.951801	−	0.306715i	$-0.0992300\pi$
$200$	−5.57978	−	6.36932i	−0.394550	−	0.450379i
$201$		−	1.35724i		−	0.0957321i
$202$	−5.96317	−	10.8740i	−0.419567	−	0.765090i
$203$	−3.36979	+	3.36979i	−0.236513	+	0.236513i
$204$	0.277446	+	1.25357i	0.0194251	+	0.0877675i
$205$	11.5846	+	11.5846i	0.809105	+	0.809105i
$206$	5.62021	+	1.63922i	0.391578	+	0.114210i
$207$	19.6499			1.36576
$208$	−1.37073	+	3.75780i	−0.0950431	+	0.260557i
$209$	−0.128057			−0.00885791
$210$	−0.518133	−	0.151121i	−0.0357546	−	0.0104283i
$211$	14.0307	+	14.0307i	0.965914	+	0.965914i	0.999438	−	0.0335239i	$-0.0106730\pi$
$211$	14.0307	+	14.0307i	0.965914	+	0.965914i	−0.0335239	+	0.999438i	$0.510673\pi$
$212$	0.385103	−	0.0852328i	0.0264490	−	0.00585381i
$213$	2.17290	−	2.17290i	0.148885	−	0.148885i
$214$	4.49720	+	8.20074i	0.307422	+	0.560591i
$215$		−	19.4000i		−	1.32307i
$216$	−0.220911	+	3.34336i	−0.0150311	+	0.227487i
$217$		−	1.53832i		−	0.104428i
$218$	0.911375	−	0.499788i	0.0617261	−	0.0338499i
$219$	1.34137	−	1.34137i	0.0906417	−	0.0906417i
$220$	−0.673439	+	1.05627i	−0.0454033	+	0.0712134i
$221$	2.28395	+	2.28395i	0.153635	+	0.153635i
$222$	0.263863	−	0.904680i	0.0177093	−	0.0607181i
$223$	16.5896			1.11092			0.555460	−	0.831543i	$-0.312542\pi$
$223$	16.5896			1.11092			0.555460	+	0.831543i	$0.312542\pi$
$224$	0.581104	+	3.79775i	0.0388266	+	0.253748i
$225$	−8.86311			−0.590874
$226$	−5.72639	+	19.6335i	−0.380914	+	1.30600i
$227$	−16.7443	−	16.7443i	−1.11136	−	1.11136i	−0.992967	−	0.118395i	$-0.962225\pi$
$227$	−16.7443	−	16.7443i	−1.11136	−	1.11136i	−0.118395	−	0.992967i	$-0.537775\pi$
$228$	0.123526	−	0.193746i	0.00818069	−	0.0128311i
$229$	18.4675	−	18.4675i	1.22037	−	1.22037i	0.252867	−	0.967501i	$-0.418627\pi$
$229$	18.4675	−	18.4675i	1.22037	−	1.22037i	0.967501	−	0.252867i	$-0.0813734\pi$
$230$	−23.2699	+	12.7609i	−1.53437	+	0.841432i
$231$			0.0299029i			0.00196747i
$232$	−19.8034	−	1.30850i	−1.30016	−	0.0859074i
$233$			4.09531i			0.268293i	0.990962	+	0.134146i	$0.0428292\pi$
$233$			4.09531i			0.268293i	−0.990962	+	0.134146i	$0.957171\pi$
$234$	2.01315	+	3.67102i	0.131603	+	0.239982i
$235$	−25.7406	+	25.7406i	−1.67913	+	1.67913i
$236$	2.57065	−	0.568949i	0.167335	−	0.0370355i
$237$	2.03177	+	2.03177i	0.131978	+	0.131978i
$238$	2.97828	+	0.868659i	0.193053	+	0.0563068i
$239$	−21.7926			−1.40964			−0.704822	−	0.709384i	$-0.748973\pi$
$239$	−21.7926			−1.40964			−0.704822	+	0.709384i	$0.748973\pi$
$240$	−0.948481	−	2.03777i	−0.0612242	−	0.131538i
$241$	5.37983			0.346545			0.173273	−	0.984874i	$-0.444566\pi$
$241$	5.37983			0.346545			0.173273	+	0.984874i	$0.444566\pi$
$242$	−14.8675	−	4.33632i	−0.955717	−	0.278749i
$243$	3.72807	+	3.72807i	0.239156	+	0.239156i
$244$	0.992065	+	4.48240i	0.0635105	+	0.286956i
$245$	13.0724	−	13.0724i	0.835164	−	0.835164i
$246$	0.783127	+	1.42805i	0.0499304	+	0.0910491i
$247$		−	0.578055i		−	0.0367808i
$248$	4.81884	−	4.22150i	0.305997	−	0.268066i
$249$		−	1.20341i		−	0.0762631i
$250$	−7.03354	+	3.85712i	−0.444840	+	0.243946i
$251$	16.7207	−	16.7207i	1.05540	−	1.05540i	0.0570276	−	0.998373i	$-0.481838\pi$
$251$	16.7207	−	16.7207i	1.05540	−	1.05540i	0.998373	−	0.0570276i	$-0.0181623\pi$
$252$	3.39081	+	2.16187i	0.213601	+	0.136185i
$253$	1.03972	+	1.03972i	0.0653666	+	0.0653666i
$254$	−6.95558	+	23.8479i	−0.436432	+	1.49635i
$255$	−1.81501			−0.113661
$256$	−10.3019	+	12.2422i	−0.643867	+	0.765137i
$257$	17.0701			1.06480			0.532401	−	0.846492i	$-0.321290\pi$
$257$	17.0701			1.06480			0.532401	+	0.846492i	$0.321290\pi$
$258$	0.540003	−	1.85145i	0.0336191	−	0.115266i
$259$	−1.61016	−	1.61016i	−0.100050	−	0.100050i
$260$	−4.76802	−	3.03993i	−0.295700	−	0.188528i
$261$	−14.6890	+	14.6890i	−0.909224	+	0.909224i
$262$	25.9243	−	14.2166i	1.60161	−	0.878306i
$263$		−	12.6474i		−	0.779871i	−0.920842	−	0.389935i	$-0.872497\pi$
$263$		−	12.6474i		−	0.779871i	0.920842	−	0.389935i	$-0.127503\pi$
$264$	−0.0936717	+	0.0820603i	−0.00576510	+	0.00505046i
$265$			0.557580i			0.0342519i
$266$	−0.266966	−	0.486819i	−0.0163688	−	0.0298488i
$267$	1.64520	−	1.64520i	0.100685	−	0.100685i
$268$	−2.95141	−	13.3352i	−0.180286	−	0.814577i
$269$	7.99978	+	7.99978i	0.487755	+	0.487755i	0.907597	−	0.419842i	$-0.137915\pi$
$269$	7.99978	+	7.99978i	0.487755	+	0.487755i	−0.419842	+	0.907597i	$0.637915\pi$
$270$	−4.54723	−	1.32627i	−0.276736	−	0.0807140i
$271$	−15.8222			−0.961131			−0.480565	−	0.876959i	$-0.659569\pi$
$271$	−15.8222			−0.961131			−0.480565	+	0.876959i	$0.659569\pi$
$272$	5.45197	+	11.7133i	0.330574	+	0.710225i
$273$	−0.134983			−0.00816953
$274$	10.4536	+	3.04895i	0.631526	+	0.184194i
$275$	−0.468966	−	0.468966i	−0.0282797	−	0.0282797i
$276$	−2.57598	+	0.570129i	−0.155056	+	0.0343177i
$277$	6.76065	−	6.76065i	0.406208	−	0.406208i	−0.474206	−	0.880414i	$-0.657265\pi$
$277$	6.76065	−	6.76065i	0.406208	−	0.406208i	0.880414	+	0.474206i	$0.157265\pi$
$278$	10.6806	+	19.4763i	0.640578	+	1.16811i
$279$		−	6.70557i		−	0.401452i
$280$	−5.41941	−	0.358086i	−0.323872	−	0.0213997i
$281$			3.04201i			0.181471i	0.995875	+	0.0907357i	$0.0289218\pi$
$281$			3.04201i			0.181471i	−0.995875	+	0.0907357i	$0.971078\pi$
$282$	−3.17307	+	1.74008i	−0.188954	+	0.103620i
$283$	9.92758	−	9.92758i	0.590134	−	0.590134i	−0.347534	−	0.937667i	$-0.612981\pi$
$283$	9.92758	−	9.92758i	0.590134	−	0.590134i	0.937667	+	0.347534i	$0.112981\pi$
$284$	16.6242	−	26.0744i	0.986463	−	1.54723i
$285$	0.229685	+	0.229685i	0.0136053	+	0.0136053i
$286$	−0.0877214	+	0.300761i	−0.00518708	+	0.0177844i
$287$	3.93548			0.232304
$288$	2.53304	+	16.5544i	0.149261	+	0.975480i
$289$	−6.56712			−0.386301
$290$	7.85575	−	26.9342i	0.461306	−	1.58163i
$291$	−0.702840	−	0.702840i	−0.0412012	−	0.0412012i
$292$	10.2624	−	16.0963i	0.600564	−	0.941963i
$293$	12.9054	−	12.9054i	0.753943	−	0.753943i	−0.221270	−	0.975213i	$-0.571020\pi$
$293$	12.9054	−	12.9054i	0.753943	−	0.753943i	0.975213	+	0.221270i	$0.0710201\pi$
$294$	1.61145	−	0.883701i	0.0939815	−	0.0515385i
$295$			3.72198i			0.216702i
$296$	0.625231	−	9.46250i	0.0363408	−	0.549997i
$297$			0.262434i			0.0152279i
$298$	−14.3956	−	26.2506i	−0.833913	−	1.52066i
$299$	−4.69333	+	4.69333i	−0.271422	+	0.271422i
$300$	1.16190	−	0.257157i	0.0670822	−	0.0148470i
$301$	−3.29523	−	3.29523i	−0.189934	−	0.189934i
$302$	5.47337	+	1.59639i	0.314957	+	0.0918619i
$303$	1.74288			0.100126
$304$	0.792358	−	2.17222i	0.0454448	−	0.124585i
$305$	−6.48995			−0.371613
$306$	12.9824	+	3.78650i	0.742152	+	0.216460i
$307$	15.5129	+	15.5129i	0.885366	+	0.885366i	0.994074	−	0.108708i	$-0.0346712\pi$
$307$	15.5129	+	15.5129i	0.885366	+	0.885366i	−0.108708	+	0.994074i	$0.534671\pi$
$308$	0.0650261	+	0.293804i	0.00370521	+	0.0167410i
$309$	−0.581771	+	0.581771i	−0.0330958	+	0.0330958i
$310$	4.35469	+	7.94088i	0.247330	+	0.451012i
$311$			9.93237i			0.563213i	0.959530	+	0.281607i	$0.0908673\pi$
$311$			9.93237i			0.563213i	−0.959530	+	0.281607i	$0.909133\pi$
$312$	−0.370423	−	0.422837i	−0.0209711	−	0.0239384i
$313$		−	7.51287i		−	0.424653i	−0.977199	−	0.212326i	$-0.931896\pi$
$313$		−	7.51287i		−	0.424653i	0.977199	−	0.212326i	$-0.0681040\pi$
$314$	2.01056	−	1.10257i	0.113462	−	0.0622216i
$315$	−4.01979	+	4.01979i	−0.226489	+	0.226489i
$316$	24.3809	+	15.5444i	1.37153	+	0.874443i
$317$	15.5411	+	15.5411i	0.872874	+	0.872874i	0.992785	−	0.119911i	$-0.0382610\pi$
$317$	15.5411	+	15.5411i	0.872874	+	0.872874i	−0.119911	+	0.992785i	$0.538261\pi$
$318$	−0.0155204	+	0.0532131i	−0.000870341	+	0.00298405i
$319$	−1.55445			−0.0870325
$320$	−13.7504	−	17.9591i	−0.768669	−	1.00395i
$321$	−1.31442			−0.0733636
$322$	−1.78502	+	6.12011i	−0.0994753	+	0.341061i
$323$	−1.32025	−	1.32025i	−0.0734607	−	0.0734607i
$324$	14.5807	+	9.29619i	0.810041	+	0.516455i
$325$	2.11693	−	2.11693i	0.117426	−	0.117426i
$326$	9.63492	−	5.28369i	0.533629	−	0.292637i
$327$			0.146075i			0.00807799i
$328$	10.7998	+	12.3280i	0.596321	+	0.680699i
$329$			8.74449i			0.482099i
$330$	−0.0846493	−	0.154360i	−0.00465979	−	0.00849723i
$331$	−14.3724	+	14.3724i	−0.789978	+	0.789978i	−0.981490	−	0.191512i	$-0.938661\pi$
$331$	−14.3724	+	14.3724i	−0.789978	+	0.789978i	0.191512	+	0.981490i	$0.438661\pi$
$332$	−2.61691	−	11.8238i	−0.143621	−	0.648917i
$333$	−7.01870	−	7.01870i	−0.384623	−	0.384623i
$334$	5.47146	+	1.59583i	0.299385	+	0.0873201i
$335$	19.3077			1.05489
$336$	−0.507239	−	0.185025i	−0.0276722	−	0.0100939i
$337$	−15.5349			−0.846242			−0.423121	−	0.906073i	$-0.639065\pi$
$337$	−15.5349			−0.846242			−0.423121	+	0.906073i	$0.639065\pi$
$338$	−1.35765	−	0.395977i	−0.0738462	−	0.0215383i
$339$	−2.03234	−	2.03234i	−0.110382	−	0.110382i
$340$	−17.8330	+	3.94688i	−0.967129	+	0.214050i
$341$	0.354806	−	0.354806i	0.0192138	−	0.0192138i
$342$	−1.16371	−	2.12205i	−0.0629262	−	0.114747i
$343$		−	9.19507i		−	0.496487i
$344$	1.27955	−	19.3653i	0.0689888	−	1.04410i
$345$		−	3.72970i		−	0.200800i
$346$	21.5086	−	11.7951i	1.15631	−	0.634107i
$347$	−8.58983	+	8.58983i	−0.461126	+	0.461126i	−0.899024	−	0.437898i	$-0.855723\pi$
$347$	−8.58983	+	8.58983i	−0.461126	+	0.461126i	0.437898	+	0.899024i	$0.355723\pi$
$348$	1.49944	−	2.35182i	0.0803785	−	0.126071i
$349$	−11.3669	−	11.3669i	−0.608455	−	0.608455i	0.334087	−	0.942542i	$-0.391572\pi$
$349$	−11.3669	−	11.3669i	−0.608455	−	0.608455i	−0.942542	+	0.334087i	$0.891572\pi$
$350$	0.805135	−	2.76048i	0.0430363	−	0.147554i
$351$	−1.18463			−0.0632311
$352$	−0.741903	+	1.00996i	−0.0395435	+	0.0538310i
$353$	−27.9205			−1.48606			−0.743030	−	0.669258i	$-0.766612\pi$
$353$	−27.9205			−1.48606			−0.743030	+	0.669258i	$0.766612\pi$
$354$	−0.103602	+	0.355211i	−0.00550641	+	0.0188792i
$355$	30.9111	+	30.9111i	1.64059	+	1.64059i
$356$	12.5869	−	19.7421i	0.667106	−	1.04633i
$357$	−0.308294	+	0.308294i	−0.0163167	+	0.0163167i
$358$	16.7377	−	9.17879i	0.884616	−	0.485114i
$359$			3.68447i			0.194459i	0.995262	+	0.0972293i	$0.0309980\pi$
$359$			3.68447i			0.194459i	−0.995262	+	0.0972293i	$0.969002\pi$
$360$	−23.6233	−	1.56090i	−1.24506	−	0.0822666i
$361$		−	18.6659i		−	0.982413i
$362$	−11.0594	−	20.1671i	−0.581271	−	1.05996i
$363$	1.53899	−	1.53899i	0.0807763	−	0.0807763i
$364$	−1.32624	+	0.293530i	−0.0695139	+	0.0153852i
$365$	19.0821	+	19.0821i	0.998800	+	0.998800i
$366$	−0.619374	−	0.180649i	−0.0323752	−	0.00944269i
$367$	17.4401			0.910366			0.455183	−	0.890398i	$-0.349574\pi$
$367$	17.4401			0.910366			0.455183	+	0.890398i	$0.349574\pi$
$368$	−24.0699	+	11.2033i	−1.25473	+	0.584014i
$369$	17.1548			0.893043
$370$	12.8697	+	3.75365i	0.669066	+	0.195143i
$371$	0.0947094	+	0.0947094i	0.00491707	+	0.00491707i
$372$	0.194557	+	0.879059i	0.0100873	+	0.0455771i
$373$	2.37851	−	2.37851i	0.123155	−	0.123155i	−0.642843	−	0.765998i	$-0.722245\pi$
$373$	2.37851	−	2.37851i	0.123155	−	0.123155i	0.765998	+	0.642843i	$0.222245\pi$
$374$	0.486573	+	0.887276i	0.0251601	+	0.0458800i
$375$		−	1.12734i		−	0.0582155i
$376$	−27.3923	+	23.9968i	−1.41265	+	1.23754i
$377$		−	7.01684i		−	0.361385i
$378$	−0.997660	+	0.547106i	−0.0513141	+	0.0281401i
$379$	−9.83792	+	9.83792i	−0.505340	+	0.505340i	−0.913093	−	0.407752i	$-0.866313\pi$
$379$	−9.83792	+	9.83792i	−0.505340	+	0.505340i	0.407752	+	0.913093i	$0.366313\pi$
$380$	2.75618	+	1.75725i	0.141389	+	0.0901448i
$381$	−2.46859	−	2.46859i	−0.126470	−	0.126470i
$382$	−5.14533	+	17.6412i	−0.263258	+	0.902605i
$383$	−19.9506			−1.01943			−0.509715	−	0.860344i	$-0.670249\pi$
$383$	−19.9506			−1.01943			−0.509715	+	0.860344i	$0.670249\pi$
$384$	−0.812381	−	2.09669i	−0.0414566	−	0.106996i
$385$	−0.425391			−0.0216800
$386$	4.70942	−	16.1467i	0.239703	−	0.821845i
$387$	−14.3640	−	14.3640i	−0.730161	−	0.730161i
$388$	−8.43396	−	5.37720i	−0.428169	−	0.272986i
$389$	−17.8948	+	17.8948i	−0.907300	+	0.907300i	−0.996054	−	0.0887536i	$-0.971712\pi$
$389$	−17.8948	+	17.8948i	−0.907300	+	0.907300i	0.0887536	+	0.996054i	$0.471712\pi$
$390$	0.696785	−	0.382110i	0.0352831	−	0.0193489i
$391$			21.4387i			1.08420i
$392$	13.9112	−	12.1868i	0.702623	−	0.615526i
$393$			4.15516i			0.209600i
$394$	−9.63931	−	17.5775i	−0.485621	−	0.885541i
$395$	−28.9035	+	28.9035i	−1.45429	+	1.45429i
$396$	0.283450	+	1.28070i	0.0142439	+	0.0643574i
$397$	6.59106	+	6.59106i	0.330796	+	0.330796i	0.852889	−	0.522093i	$-0.174849\pi$
$397$	6.59106	+	6.59106i	0.330796	+	0.330796i	−0.522093	+	0.852889i	$0.674849\pi$
$398$	11.7484	+	3.42659i	0.588894	+	0.171760i
$399$	0.0780275			0.00390626
$400$	10.8567	−	5.05327i	0.542837	−	0.252663i
$401$	11.1823			0.558420			0.279210	−	0.960230i	$-0.409927\pi$
$401$	11.1823			0.558420			0.279210	+	0.960230i	$0.409927\pi$
$402$	1.84265	+	0.537435i	0.0919029	+	0.0268048i
$403$	1.60161	+	1.60161i	0.0797817	+	0.0797817i
$404$	17.1243	−	3.79003i	0.851965	−	0.188561i
$405$	−17.2854	+	17.2854i	−0.858918	+	0.858918i
$406$	−3.24062	−	5.90935i	−0.160829	−	0.293276i
$407$		−	0.742750i		−	0.0368167i
$408$	−1.81177	−	0.119712i	−0.0896959	−	0.00592662i
$409$			1.96840i			0.0973312i	0.998815	+	0.0486656i	$0.0154969\pi$
$409$			1.96840i			0.0973312i	−0.998815	+	0.0486656i	$0.984503\pi$
$410$	−20.3151	+	11.1406i	−1.00329	+	0.550193i
$411$	−1.08210	+	1.08210i	−0.0533759	+	0.0533759i
$412$	−4.45095	+	6.98116i	−0.219283	+	0.343937i
$413$	0.632208	+	0.632208i	0.0311089	+	0.0311089i
$414$	−7.78093	+	26.6776i	−0.382412	+	1.31113i
$415$	17.1194			0.840359
$416$	−4.55899	−	3.34897i	−0.223523	−	0.164197i
$417$	−3.12166			−0.152868
$418$	0.0507078	−	0.173857i	0.00248020	−	0.00850360i
$419$	−23.5212	−	23.5212i	−1.14909	−	1.14909i	−0.986733	−	0.162353i	$-0.948092\pi$
$419$	−23.5212	−	23.5212i	−1.14909	−	1.14909i	−0.162353	−	0.986733i	$-0.551908\pi$
$420$	0.410338	−	0.643601i	0.0200224	−	0.0314045i
$421$	12.6222	−	12.6222i	0.615168	−	0.615168i	−0.329120	−	0.944288i	$-0.606752\pi$
$421$	12.6222	−	12.6222i	0.615168	−	0.615168i	0.944288	+	0.329120i	$0.106752\pi$
$422$	−24.6046	+	13.4929i	−1.19773	+	0.656824i
$423$			38.1173i			1.85333i
$424$	−0.0367760	+	0.556583i	−0.00178600	+	0.0270301i
$425$		−	9.66993i		−	0.469061i
$426$	2.08961	+	3.81045i	0.101242	+	0.184617i
$427$	−1.10237	+	1.10237i	−0.0533473	+	0.0533473i
$428$	−12.9145	+	2.85830i	−0.624246	+	0.138161i
$429$	−0.0311331	−	0.0311331i	−0.00150312	−	0.00150312i
$430$	26.3383	+	7.68194i	1.27014	+	0.370456i
$431$	19.4823			0.938427			0.469214	−	0.883085i	$-0.344537\pi$
$431$	19.4823			0.938427			0.469214	+	0.883085i	$0.344537\pi$
$432$	−4.45162	−	1.62381i	−0.214179	−	0.0781258i
$433$	−25.4515			−1.22312			−0.611560	−	0.791198i	$-0.709458\pi$
$433$	−25.4515			−1.22312			−0.611560	+	0.791198i	$0.709458\pi$
$434$	2.08850	+	0.609142i	0.100251	+	0.0292397i
$435$	2.78807	+	2.78807i	0.133678	+	0.133678i
$436$	0.317652	+	1.43523i	0.0152128	+	0.0687350i
$437$	2.71300	−	2.71300i	0.129781	−	0.129781i
$438$	1.28996	+	2.35227i	0.0616366	+	0.112396i
$439$		−	7.94626i		−	0.379254i	−0.981856	−	0.189627i	$-0.939272\pi$
$439$		−	7.94626i		−	0.379254i	0.981856	−	0.189627i	$-0.0607279\pi$
$440$	−1.16737	−	1.33255i	−0.0556521	−	0.0635268i
$441$		−	19.3579i		−	0.921805i
$442$	−4.00519	+	2.19641i	−0.190508	+	0.104472i
$443$	−6.33976	+	6.33976i	−0.301211	+	0.301211i	−0.841488	−	0.540276i	$-0.818320\pi$
$443$	−6.33976	+	6.33976i	−0.301211	+	0.301211i	0.540276	+	0.841488i	$0.318320\pi$
$444$	1.12375	+	0.716465i	0.0533309	+	0.0340019i
$445$	23.4042	+	23.4042i	1.10947	+	1.10947i
$446$	−6.56909	+	22.5228i	−0.311056	+	1.06648i
$447$	4.20746			0.199006
$448$	−5.38611	−	0.714891i	−0.254470	−	0.0337754i
$449$	33.5335			1.58254			0.791271	−	0.611466i	$-0.209420\pi$
$449$	33.5335			1.58254			0.791271	+	0.611466i	$0.209420\pi$
$450$	3.50959	−	12.0330i	0.165444	−	0.567239i
$451$	0.907697	+	0.907697i	0.0427418	+	0.0427418i
$452$	−24.3878	−	15.5488i	−1.14710	−	0.731355i
$453$	−0.566572	+	0.566572i	−0.0266199	+	0.0266199i
$454$	29.3633	−	16.1025i	1.37809	−	0.755728i
$455$		−	1.92023i		−	0.0900218i
$456$	0.214125	+	0.244423i	0.0100273	+	0.0114462i
$457$		−	28.3905i		−	1.32805i	−0.747709	−	0.664026i	$-0.768846\pi$
$457$		−	28.3905i		−	1.32805i	0.747709	−	0.664026i	$-0.231154\pi$
$458$	17.7596	+	32.3851i	0.829853	+	1.51325i
$459$	−2.70565	+	2.70565i	−0.126289	+	0.126289i
$460$	−8.11050	−	36.6453i	−0.378154	−	1.70859i
$461$	8.59677	+	8.59677i	0.400392	+	0.400392i	0.878371	−	0.477979i	$-0.158631\pi$
$461$	8.59677	+	8.59677i	0.400392	+	0.400392i	−0.477979	+	0.878371i	$0.658631\pi$
$462$	−0.0405976	−	0.0118409i	−0.00188877	−	0.000550888i
$463$	−37.6166			−1.74819			−0.874096	−	0.485754i	$-0.838545\pi$
$463$	−37.6166			−1.74819			−0.874096	+	0.485754i	$0.838545\pi$
$464$	9.61819	−	26.3679i	0.446513	−	1.22410i
$465$	−1.27277			−0.0590231
$466$	−5.55998	−	1.62165i	−0.257561	−	0.0751215i
$467$	9.13094	+	9.13094i	0.422530	+	0.422530i	0.886074	−	0.463544i	$-0.153422\pi$
$467$	9.13094	+	9.13094i	0.422530	+	0.422530i	−0.463544	+	0.886074i	$0.653422\pi$
$468$	−5.78110	+	1.27950i	−0.267231	+	0.0591449i
$469$	3.27957	−	3.27957i	0.151436	−	0.151436i
$470$	−24.7539	−	45.1393i	−1.14181	−	2.08212i
$471$			0.322253i			0.0148486i
$472$	−0.245489	+	3.71533i	−0.0112995	+	0.171012i
$473$		−	1.52006i		−	0.0698923i
$474$	−3.56296	+	1.95389i	−0.163652	+	0.0897452i
$475$	−1.22370	+	1.22370i	−0.0561473	+	0.0561473i
$476$	−2.35866	+	3.69948i	−0.108109	+	0.169565i
$477$	0.412839	+	0.412839i	0.0189026	+	0.0189026i
$478$	8.62937	−	29.5866i	0.394698	−	1.35326i
$479$	−26.5301			−1.21219			−0.606096	−	0.795392i	$-0.707265\pi$
$479$	−26.5301			−1.21219			−0.606096	+	0.795392i	$0.707265\pi$
$480$	3.14215	−	0.480789i	0.143419	−	0.0219449i
$481$	3.35279			0.152874
$482$	−2.13029	+	7.30390i	−0.0970321	+	0.332684i
$483$	−0.633519	−	0.633519i	−0.0288261	−	0.0288261i
$484$	11.7744	−	18.4677i	0.535198	−	0.839440i
$485$	9.99841	−	9.99841i	0.454005	−	0.454005i
$486$	−6.53762	+	3.58516i	−0.296553	+	0.162626i
$487$			8.92119i			0.404258i	0.979359	+	0.202129i	$0.0647860\pi$
$487$			8.92119i			0.404258i	−0.979359	+	0.202129i	$0.935214\pi$
$488$	−6.47834	−	0.428054i	−0.293261	−	0.0193771i
$489$			1.54429i			0.0698352i
$490$	12.5713	+	22.9240i	0.567913	+	1.03560i
$491$	−27.4742	+	27.4742i	−1.23989	+	1.23989i	−0.279849	+	0.960044i	$0.590285\pi$
$491$	−27.4742	+	27.4742i	−1.23989	+	1.23989i	−0.960044	+	0.279849i	$0.909715\pi$
$492$	−2.24889	+	0.497734i	−0.101388	+	0.0224396i
$493$	−16.0261	−	16.0261i	−0.721780	−	0.721780i
$494$	0.784794	+	0.228897i	0.0353096	+	0.0102985i
$495$	−1.85429			−0.0833440
$496$	3.82315	+	8.21390i	0.171665	+	0.368815i
$497$	10.5010			0.471034
$498$	1.63381	+	0.476524i	0.0732126	+	0.0213535i
$499$	−30.1451	−	30.1451i	−1.34948	−	1.34948i	−0.886226	−	0.463253i	$-0.846682\pi$
$499$	−30.1451	−	30.1451i	−1.34948	−	1.34948i	−0.463253	−	0.886226i	$-0.653318\pi$
$500$	−2.45148	−	11.0764i	−0.109634	−	0.495351i
$501$	−0.566374	+	0.566374i	−0.0253037	+	0.0253037i
$502$	16.0798	+	29.3218i	0.717675	+	1.30869i
$503$		−	33.6172i		−	1.49892i	−0.662051	−	0.749459i	$-0.730314\pi$
$503$		−	33.6172i		−	1.49892i	0.662051	−	0.749459i	$-0.269686\pi$
$504$	−4.27773	+	3.74747i	−0.190545	+	0.166926i
$505$			24.7938i			1.10331i
$506$	−1.82328	+	0.999866i	−0.0810546	+	0.0444495i
$507$	0.140536	−	0.140536i	0.00624141	−	0.00624141i
$508$	−29.6227	−	18.8864i	−1.31430	−	0.837950i
$509$	1.85529	+	1.85529i	0.0822344	+	0.0822344i	0.747028	−	0.664793i	$-0.231480\pi$
$509$	1.85529	+	1.85529i	0.0822344	+	0.0822344i	−0.664793	+	0.747028i	$0.731480\pi$
$510$	0.718704	−	2.46415i	0.0318248	−	0.109114i
$511$	6.48247			0.286768
$512$	−12.5413	−	18.8339i	−0.554250	−	0.832350i
$513$	0.684784			0.0302339
$514$	−6.75937	+	23.1751i	−0.298143	+	1.02221i
$515$	−8.27613	−	8.27613i	−0.364690	−	0.364690i
$516$	2.29979	+	1.46627i	0.101242	+	0.0645487i
$517$	−2.01687	+	2.01687i	−0.0887018	+	0.0887018i
$518$	2.82361	−	1.54844i	0.124062	−	0.0680345i
$519$			3.44740i			0.151324i
$520$	6.01517	−	5.26954i	0.263783	−	0.231085i
$521$		−	37.1544i		−	1.62776i	−0.581031	−	0.813881i	$-0.697350\pi$
$521$		−	37.1544i		−	1.62776i	0.581031	−	0.813881i	$-0.302650\pi$
$522$	−14.1259	−	25.7589i	−0.618275	−	1.12744i
$523$	−17.4018	+	17.4018i	−0.760928	+	0.760928i	−0.976490	−	0.215562i	$-0.930842\pi$
$523$	−17.4018	+	17.4018i	−0.760928	+	0.760928i	0.215562	+	0.976490i	$0.430842\pi$
$524$	9.03570	+	40.8255i	0.394726	+	1.78347i
$525$	0.285749	+	0.285749i	0.0124711	+	0.0124711i
$526$	17.1707	+	5.00807i	0.748676	+	0.218362i
$527$	7.31599			0.318690
$528$	−0.0743169	−	0.159667i	−0.00323423	−	0.00694862i
$529$	−21.0547			−0.915421
$530$	−0.756996	−	0.220789i	−0.0328818	−	0.00959047i
$531$	2.75580	+	2.75580i	0.119592	+	0.119592i
$532$	0.766640	−	0.169677i	0.0332381	−	0.00735641i
$533$	−4.09737	+	4.09737i	−0.177477	+	0.177477i
$534$	1.58214	+	2.88506i	0.0684658	+	0.124849i
$535$		−	18.6986i		−	0.808409i
$536$	19.2732	+	1.27347i	0.832475	+	0.0550054i
$537$			2.68273i			0.115768i
$538$	−14.0286	+	7.69313i	−0.604816	+	0.331675i
$539$	1.02427	−	1.02427i	0.0441184	−	0.0441184i
$540$	3.60120	−	5.64836i	0.154971	−	0.243067i
$541$	−11.4555	−	11.4555i	−0.492511	−	0.492511i	0.416586	−	0.909096i	$-0.363227\pi$
$541$	−11.4555	−	11.4555i	−0.492511	−	0.492511i	−0.909096	+	0.416586i	$0.863227\pi$
$542$	6.26524	−	21.4810i	0.269115	−	0.922686i
$543$	3.23239			0.138715
$544$	−18.0614	+	2.76362i	−0.774377	+	0.118489i
$545$	−2.07803			−0.0890131
$546$	0.0534501	−	0.183259i	0.00228745	−	0.00784275i
$547$	5.93459	+	5.93459i	0.253745	+	0.253745i	0.822504	−	0.568759i	$-0.192576\pi$
$547$	5.93459	+	5.93459i	0.253745	+	0.253745i	−0.568759	+	0.822504i	$0.692576\pi$
$548$	−8.27879	+	12.9850i	−0.353652	+	0.554691i
$549$	−4.80524	+	4.80524i	−0.205082	+	0.205082i
$550$	0.822390	−	0.450990i	0.0350668	−	0.0192303i
$551$			4.05612i			0.172796i
$552$	0.245998	−	3.72303i	0.0104704	−	0.158463i
$553$			9.81896i			0.417545i
$554$	6.50151	+	11.8556i	0.276223	+	0.503698i
$555$	−1.33220	+	1.33220i	−0.0565488	+	0.0565488i
$556$	−30.6711	+	6.78828i	−1.30074	+	0.287887i
$557$	−6.71440	−	6.71440i	−0.284498	−	0.284498i	0.550402	−	0.834900i	$-0.314475\pi$
$557$	−6.71440	−	6.71440i	−0.284498	−	0.284498i	−0.834900	+	0.550402i	$0.814475\pi$
$558$	9.10379	+	2.65526i	0.385394	+	0.112406i
$559$	6.86158			0.290214
$560$	2.63212	−	7.21585i	0.111227	−	0.304925i
$561$	−0.142213			−0.00600423
$562$	−4.12998	−	1.20457i	−0.174213	−	0.0508117i
$563$	25.1933	+	25.1933i	1.06177	+	1.06177i	0.997962	+	0.0638074i	$0.0203243\pi$
$563$	25.1933	+	25.1933i	1.06177	+	1.06177i	0.0638074	+	0.997962i	$0.479676\pi$
$564$	−1.10595	−	4.99694i	−0.0465688	−	0.210409i
$565$	28.9116	−	28.9116i	1.21632	−	1.21632i
$566$	9.54704	+	17.4092i	0.401292	+	0.731765i
$567$			5.87212i			0.246606i
$568$	28.8170	+	32.8946i	1.20914	+	1.38023i
$569$		−	30.2477i		−	1.26805i	−0.773313	−	0.634024i	$-0.781402\pi$
$569$		−	30.2477i		−	1.26805i	0.773313	−	0.634024i	$-0.218598\pi$
$570$	−0.402780	+	0.220880i	−0.0168706	+	0.00925167i
$571$	19.8878	−	19.8878i	0.832278	−	0.832278i	−0.155550	−	0.987828i	$-0.549715\pi$
$571$	19.8878	−	19.8878i	0.832278	−	0.832278i	0.987828	+	0.155550i	$0.0497149\pi$
$572$	−0.373592	−	0.238189i	−0.0156206	−	0.00995919i
$573$	−1.82612	−	1.82612i	−0.0762872	−	0.0762872i
$574$	−1.55836	+	5.34299i	−0.0650447	+	0.223012i
$575$	19.8709			0.828673
$576$	−23.4781	−	3.11622i	−0.978254	−	0.129842i
$577$	22.2260			0.925280			0.462640	−	0.886546i	$-0.346902\pi$
$577$	22.2260			0.925280			0.462640	+	0.886546i	$0.346902\pi$
$578$	2.60043	−	8.91582i	0.108164	−	0.370849i
$579$	1.67141	+	1.67141i	0.0694615	+	0.0694615i
$580$	33.4564	+	21.3307i	1.38920	+	0.885708i
$581$	2.90787	−	2.90787i	0.120639	−	0.120639i
$582$	1.23252	−	0.675899i	0.0510894	−	0.0280169i
$583$			0.0436884i			0.00180939i
$584$	17.7893	+	20.3065i	0.736128	+	0.840289i
$585$		−	8.37031i		−	0.346070i
$586$	12.4107	+	22.6312i	0.512683	+	0.934888i
$587$	22.5799	−	22.5799i	0.931972	−	0.931972i	−0.0658567	−	0.997829i	$-0.520978\pi$
$587$	22.5799	−	22.5799i	0.931972	−	0.931972i	0.997829	+	0.0658567i	$0.0209780\pi$
$588$	0.561656	+	2.53770i	0.0231623	+	0.104653i
$589$	−0.925817	−	0.925817i	−0.0381476	−	0.0381476i
$590$	−5.05314	−	1.47382i	−0.208034	−	0.0606763i
$591$	2.81732			0.115889
$592$	12.5991	+	4.59578i	0.517822	+	0.188885i
$593$	−20.2111			−0.829969			−0.414984	−	0.909829i	$-0.636213\pi$
$593$	−20.2111			−0.829969			−0.414984	+	0.909829i	$0.636213\pi$
$594$	−0.356292	−	0.103918i	−0.0146188	−	0.00426380i
$595$	−4.38572	−	4.38572i	−0.179797	−	0.179797i
$596$	41.3394	−	9.14943i	1.69333	−	0.374775i
$597$	−1.21613	+	1.21613i	−0.0497727	+	0.0497727i
$598$	−4.51343	−	8.23033i	−0.184568	−	0.336563i
$599$		−	5.65719i		−	0.231147i	−0.993299	−	0.115573i	$-0.963129\pi$
$599$		−	5.65719i		−	0.231147i	0.993299	−	0.115573i	$-0.0368705\pi$
$600$	−0.110957	+	1.67927i	−0.00452982	+	0.0685561i
$601$			13.0483i			0.532253i	0.963938	+	0.266127i	$0.0857439\pi$
$601$			13.0483i			0.532253i	−0.963938	+	0.266127i	$0.914256\pi$
$602$	5.77860	−	3.16892i	0.235518	−	0.129156i
$603$	14.2957	−	14.2957i	0.582164	−	0.582164i
$604$	−4.33466	+	6.79877i	−0.176375	+	0.276638i
$605$	21.8933	+	21.8933i	0.890091	+	0.890091i
$606$	−0.690143	+	2.36622i	−0.0280351	+	0.0961211i
$607$	11.2201			0.455410			0.227705	−	0.973730i	$-0.426878\pi$
$607$	11.2201			0.455410			0.227705	+	0.973730i	$0.426878\pi$
$608$	2.63535	+	1.93589i	0.106877	+	0.0785107i
$609$	0.947152			0.0383805
$610$	2.56987	−	8.81105i	0.104051	−	0.356749i
$611$	−9.10421	−	9.10421i	−0.368317	−	0.368317i
$612$	−10.2814	+	16.1261i	−0.415603	+	0.651858i
$613$	−18.5888	+	18.5888i	−0.750794	+	0.750794i	−0.974627	−	0.223833i	$-0.928143\pi$
$613$	−18.5888	+	18.5888i	−0.750794	+	0.750794i	0.223833	+	0.974627i	$0.428143\pi$
$614$	−27.2037	+	14.9182i	−1.09785	+	0.602051i
$615$		−	3.25611i		−	0.131299i
$616$	−0.424631	−	0.0280573i	−0.0171089	−	0.00113046i
$617$			34.2269i			1.37792i	0.724797	+	0.688962i	$0.241933\pi$
$617$			34.2269i			1.37792i	−0.724797	+	0.688962i	$0.758067\pi$
$618$	−0.559471	−	1.02021i	−0.0225052	−	0.0410388i
$619$	3.23914	−	3.23914i	0.130192	−	0.130192i	−0.639008	−	0.769200i	$-0.720655\pi$
$619$	3.23914	−	3.23914i	0.130192	−	0.130192i	0.769200	+	0.639008i	$0.220655\pi$
$620$	−12.5053	+	2.76772i	−0.502223	+	0.111154i
$621$	−5.55988	−	5.55988i	−0.223110	−	0.223110i
$622$	−13.4846	−	3.93299i	−0.540685	−	0.157699i
$623$	7.95078			0.318541
$624$	0.720742	−	0.335469i	0.0288528	−	0.0134295i
$625$	31.0062			1.24025
$626$	10.1998	+	2.97493i	0.407667	+	0.118902i
$627$	0.0179966	+	0.0179966i	0.000718716	+	0.000718716i
$628$	0.700763	+	3.16622i	0.0279635	+	0.126346i
$629$	7.65763	−	7.65763i	0.305330	−	0.305330i
$630$	−3.86570	−	7.04920i	−0.154013	−	0.280847i
$631$		−	9.90027i		−	0.394124i	−0.980391	−	0.197062i	$-0.936860\pi$
$631$		−	9.90027i		−	0.394124i	0.980391	−	0.197062i	$-0.0631400\pi$
$632$	−30.7581	+	26.9454i	−1.22349	+	1.07183i
$633$		−	3.94363i		−	0.156745i
$634$	−27.2532	+	14.9454i	−1.08236	+	0.593556i
$635$	35.1176	−	35.1176i	1.39360	−	1.39360i
$636$	−0.0660989	−	0.0421424i	−0.00262099	−	0.00167105i
$637$	4.62358	+	4.62358i	0.183193	+	0.183193i
$638$	0.615527	−	2.11039i	0.0243689	−	0.0835512i
$639$	45.7739			1.81079
$640$	29.8270	−	11.5567i	1.17901	−	0.456819i
$641$	−1.35779			−0.0536294			−0.0268147	−	0.999640i	$-0.508536\pi$
$641$	−1.35779			−0.0536294			−0.0268147	+	0.999640i	$0.508536\pi$
$642$	0.520480	−	1.78451i	0.0205417	−	0.0704291i
$643$	33.1979	+	33.1979i	1.30920	+	1.30920i	0.921996	+	0.387200i	$0.126558\pi$
$643$	33.1979	+	33.1979i	1.30920	+	1.30920i	0.387200	+	0.921996i	$0.373442\pi$
$644$	−7.60212	−	4.84685i	−0.299565	−	0.190993i
$645$	−2.72638	+	2.72638i	−0.107351	+	0.107351i
$646$	2.31522	−	1.26964i	0.0910912	−	0.0499535i
$647$			5.78691i			0.227507i	0.993509	+	0.113754i	$0.0362874\pi$
$647$			5.78691i			0.227507i	−0.993509	+	0.113754i	$0.963713\pi$
$648$	−18.3946	+	16.1144i	−0.722607	+	0.633034i
$649$			0.291631i			0.0114475i
$650$	2.03578	+	3.71229i	0.0798500	+	0.145608i
$651$	−0.216189	+	0.216189i	−0.00847313	+	0.00847313i
$652$	3.35817	+	15.1730i	0.131516	+	0.594222i
$653$	0.229194	+	0.229194i	0.00896907	+	0.00896907i	0.711577	−	0.702608i	$-0.247981\pi$
$653$	0.229194	+	0.229194i	0.00896907	+	0.00896907i	−0.702608	+	0.711577i	$0.747981\pi$
$654$	−0.198319	−	0.0578426i	−0.00775487	−	0.00226182i
$655$	−59.1102			−2.30963
$656$	−21.0135	+	9.78074i	−0.820440	+	0.381874i
$657$	28.2572			1.10242
$658$	−11.8719	−	3.46262i	−0.462815	−	0.134987i
$659$	0.0288370	+	0.0288370i	0.00112333	+	0.00112333i	0.707668	−	0.706545i	$-0.249747\pi$
$659$	0.0288370	+	0.0288370i	0.00112333	+	0.00112333i	−0.706545	+	0.707668i	$0.749747\pi$
$660$	0.243085	−	0.0538008i	0.00946208	−	0.00209419i
$661$	10.8971	−	10.8971i	0.423846	−	0.423846i	−0.462679	−	0.886526i	$-0.653112\pi$
$661$	10.8971	−	10.8971i	0.423846	−	0.423846i	0.886526	+	0.462679i	$0.153112\pi$
$662$	−13.8215	−	25.2038i	−0.537187	−	0.979572i
$663$		−	0.641954i		−	0.0249314i
$664$	17.0888	+	1.12914i	0.663174	+	0.0438190i
$665$			1.11000i			0.0430439i
$666$	12.3082	−	6.74967i	0.476932	−	0.261544i
$667$	32.9323	−	32.9323i	1.27514	−	1.27514i
$668$	−4.33315	+	6.79640i	−0.167655	+	0.262960i
$669$	−2.33143	−	2.33143i	−0.0901381	−	0.0901381i
$670$	−7.64541	+	26.2130i	−0.295368	+	1.01270i
$671$	−0.508511			−0.0196308
$672$	0.452054	−	0.615385i	0.0174383	−	0.0237390i
$673$	−47.6115			−1.83529			−0.917644	−	0.397404i	$-0.869911\pi$
$673$	−47.6115			−1.83529			−0.917644	+	0.397404i	$0.869911\pi$
$674$	6.15148	−	21.0909i	0.236946	−	0.812392i
$675$	2.50778	+	2.50778i	0.0965247	+	0.0965247i
$676$	1.07519	−	1.68640i	0.0413536	−	0.0648617i
$677$	15.4173	−	15.4173i	0.592534	−	0.592534i	−0.345781	−	0.938315i	$-0.612386\pi$
$677$	15.4173	−	15.4173i	0.592534	−	0.592534i	0.938315	+	0.345781i	$0.112386\pi$
$678$	3.56396	−	1.95444i	0.136873	−	0.0750598i
$679$		−	3.39662i		−	0.130350i
$680$	1.70299	−	25.7737i	0.0653067	−	0.988378i
$681$			4.70635i			0.180348i
$682$	0.341206	+	0.622197i	0.0130655	+	0.0238251i
$683$	−11.0824	+	11.0824i	−0.424058	+	0.424058i	−0.886598	−	0.462541i	$-0.846938\pi$
$683$	−11.0824	+	11.0824i	−0.424058	+	0.424058i	0.462541	+	0.886598i	$0.346938\pi$
$684$	3.34179	−	0.739622i	0.127777	−	0.0282801i
$685$	−15.3936	−	15.3936i	−0.588161	−	0.588161i
$686$	12.4836	+	3.64104i	0.476628	+	0.139016i
$687$	−5.19069			−0.198037
$688$	25.7845	+	9.40538i	0.983025	+	0.358577i
$689$	−0.197211			−0.00751314
$690$	5.06361	+	1.47688i	0.192768	+	0.0562237i
$691$	−20.2378	−	20.2378i	−0.769884	−	0.769884i	0.208202	−	0.978086i	$-0.433239\pi$
$691$	−20.2378	−	20.2378i	−0.769884	−	0.769884i	−0.978086	+	0.208202i	$0.933239\pi$
$692$	7.49662	+	33.8716i	0.284979	+	1.28760i
$693$	−0.314965	+	0.314965i	−0.0119645	+	0.0119645i
$694$	−8.26057	−	15.0633i	−0.313567	−	0.571796i
$695$		−	44.4079i		−	1.68449i
$696$	2.59920	+	2.96698i	0.0985222	+	0.112463i
$697$			18.7164i			0.708935i
$698$	19.9332	−	10.9312i	0.754483	−	0.413751i
$699$	0.575537	−	0.575537i	0.0217688	−	0.0217688i
$700$	3.42894	+	2.18618i	0.129602	+	0.0826297i
$701$	−20.5691	−	20.5691i	−0.776885	−	0.776885i	0.202415	−	0.979300i	$-0.435121\pi$
$701$	−20.5691	−	20.5691i	−0.776885	−	0.776885i	−0.979300	+	0.202415i	$0.935121\pi$
$702$	0.469088	−	1.60831i	0.0177046	−	0.0607019i
$703$	−1.93810			−0.0730968
$704$	−1.07739	−	1.40716i	−0.0406057	−	0.0530344i
$705$	7.23494			0.272484
$706$	11.0559	−	37.9062i	0.416094	−	1.42662i
$707$	4.21143	+	4.21143i	0.158387	+	0.158387i
$708$	−0.441226	−	0.281311i	−0.0165823	−	0.0105723i
$709$	−17.1600	+	17.1600i	−0.644458	+	0.644458i	−0.951648	−	0.307190i	$-0.900611\pi$
$709$	−17.1600	+	17.1600i	−0.644458	+	0.644458i	0.307190	+	0.951648i	$0.400611\pi$
$710$	−54.2064	+	29.7262i	−2.03433	+	1.11561i
$711$			42.8009i			1.60516i
$712$	21.8187	+	24.9060i	0.817691	+	0.933393i
$713$			15.0337i			0.563018i
$714$	−0.296477	−	0.540632i	−0.0110954	−	0.0202327i
$715$	0.442891	−	0.442891i	0.0165632	−	0.0165632i
$716$	5.83379	+	26.3585i	0.218019	+	0.985063i
$717$	3.06263	+	3.06263i	0.114376	+	0.114376i
$718$	−5.00220	−	1.45896i	−0.186680	−	0.0544481i
$719$	−37.9343			−1.41471			−0.707355	−	0.706858i	$-0.750112\pi$
$719$	−37.9343			−1.41471			−0.707355	+	0.706858i	$0.750112\pi$
$720$	11.4734	−	31.4540i	0.427590	−	1.17222i
$721$	−2.81153			−0.104707
$722$	25.3416	+	7.39125i	0.943117	+	0.275074i
$723$	−0.756058	−	0.756058i	−0.0281181	−	0.0281181i
$724$	31.7591	−	7.02907i	1.18032	−	0.261233i
$725$	−14.8541	+	14.8541i	−0.551669	+	0.551669i
$726$	1.48000	+	2.69882i	0.0549281	+	0.100162i
$727$		−	9.96189i		−	0.369466i	−0.982789	−	0.184733i	$-0.940858\pi$
$727$		−	9.96189i		−	0.369466i	0.982789	−	0.184733i	$-0.0591421\pi$
$728$	0.126652	−	1.91680i	0.00469402	−	0.0710412i
$729$			24.8903i			0.921863i
$730$	−33.4627	+	18.3506i	−1.23851	+	0.679186i
$731$	15.6715	−	15.6715i	0.579633	−	0.579633i
$732$	0.490516	−	0.769357i	0.0181300	−	0.0284362i
$733$	−18.7142	−	18.7142i	−0.691226	−	0.691226i	0.271276	−	0.962502i	$-0.412554\pi$
$733$	−18.7142	−	18.7142i	−0.691226	−	0.691226i	−0.962502	+	0.271276i	$0.912554\pi$
$734$	−6.90588	+	23.6775i	−0.254901	+	0.873952i
$735$	−3.67427			−0.135528
$736$	−5.67901	−	37.1147i	−0.209331	−	1.36806i
$737$	1.51283			0.0557258
$738$	−6.79291	+	23.2901i	−0.250051	+	0.857322i
$739$	−12.3051	−	12.3051i	−0.452651	−	0.452651i	0.443582	−	0.896234i	$-0.353707\pi$
$739$	−12.3051	−	12.3051i	−0.452651	−	0.452651i	−0.896234	+	0.443582i	$0.853707\pi$
$740$	−10.1923	+	15.9862i	−0.374675	+	0.587664i
$741$	−0.0812373	+	0.0812373i	−0.00298433	+	0.00298433i
$742$	−0.166085	+	0.0910790i	−0.00609716	+	0.00334362i
$743$			36.8246i			1.35096i	0.737377	+	0.675481i	$0.236064\pi$
$743$			36.8246i			1.35096i	−0.737377	+	0.675481i	$0.763936\pi$
$744$	−1.27049	−	0.0839471i	−0.0465784	−	0.00307765i
$745$			59.8542i			2.19289i
$746$	2.28734	+	4.17101i	0.0837454	+	0.152712i
$747$	12.6754	−	12.6754i	0.463770	−	0.463770i
$748$	−1.39728	+	0.309252i	−0.0510896	+	0.0113074i
$749$	−3.17610	−	3.17610i	−0.116052	−	0.116052i
$750$	1.53053	+	0.446401i	0.0558869	+	0.0163002i
$751$	−3.39816			−0.124001			−0.0620004	−	0.998076i	$-0.519748\pi$
$751$	−3.39816			−0.124001			−0.0620004	+	0.998076i	$0.519748\pi$
$752$	−21.7324	−	46.6913i	−0.792500	−	1.70266i
$753$	−4.69970			−0.171267
$754$	9.52638	+	2.77851i	0.346930	+	0.101187i
$755$	−8.05991	−	8.05991i	−0.293330	−	0.293330i
$756$	−0.347726	−	1.57111i	−0.0126467	−	0.0571407i
$757$	−30.2086	+	30.2086i	−1.09795	+	1.09795i	−0.103300	+	0.994650i	$0.532940\pi$
$757$	−30.2086	+	30.2086i	−1.09795	+	1.09795i	−0.994650	+	0.103300i	$0.967060\pi$
$758$	−9.46082	−	17.2520i	−0.343632	−	0.626621i
$759$		−	0.292235i		−	0.0106075i
$760$	−3.47710	+	3.04608i	−0.126128	+	0.110493i
$761$			4.28529i			0.155342i	0.996979	+	0.0776708i	$0.0247483\pi$
$761$			4.28529i			0.155342i	−0.996979	+	0.0776708i	$0.975252\pi$
$762$	4.32898	−	2.37397i	0.156823	−	0.0859998i
$763$	−0.352970	+	0.352970i	−0.0127784	+	0.0127784i
$764$	−21.9131	−	13.9711i	−0.792789	−	0.505455i
$765$	−19.1174	−	19.1174i	−0.691191	−	0.691191i
$766$	7.89999	−	27.0859i	0.285438	−	0.978652i
$767$	−1.31643			−0.0475336
$768$	3.16825	−	0.272684i	0.114324	−	0.00983963i
$769$	4.69701			0.169379			0.0846893	−	0.996407i	$-0.473010\pi$
$769$	4.69701			0.169379			0.0846893	+	0.996407i	$0.473010\pi$
$770$	0.168445	−	0.577531i	0.00607035	−	0.0208128i
$771$	−2.39895	−	2.39895i	−0.0863962	−	0.0863962i
$772$	20.0567	+	12.7874i	0.721855	+	0.460230i
$773$	19.2975	−	19.2975i	0.694082	−	0.694082i	−0.269046	−	0.963127i	$-0.586708\pi$
$773$	19.2975	−	19.2975i	0.694082	−	0.694082i	0.963127	+	0.269046i	$0.0867083\pi$
$774$	25.1890	−	13.8134i	0.905399	−	0.496511i
$775$		−	6.78097i		−	0.243580i
$776$	10.6400	−	9.32107i	0.381954	−	0.334607i
$777$			0.452570i			0.0162358i
$778$	−17.2088	−	31.3807i	−0.616966	−	1.12505i
$779$	2.36851	−	2.36851i	0.0848606	−	0.0848606i
$780$	0.242858	+	1.09729i	0.00869573	+	0.0392894i
$781$	2.42200	+	2.42200i	0.0866658	+	0.0866658i
$782$	−29.1061	−	8.48923i	−1.04083	−	0.303574i
$783$	8.31238			0.297060
$784$	11.0368	+	23.7122i	0.394173	+	0.846864i
$785$	−4.58429			−0.163620
$786$	−5.64123	−	1.64535i	−0.201216	−	0.0586876i
$787$	1.69667	+	1.69667i	0.0604798	+	0.0604798i	0.736700	−	0.676220i	$-0.236383\pi$
$787$	1.69667	+	1.69667i	0.0604798	+	0.0604798i	−0.676220	+	0.736700i	$0.736383\pi$
$788$	27.6809	−	6.12648i	0.986093	−	0.218247i
$789$	−1.77741	+	1.77741i	−0.0632774	+	0.0632774i
$790$	−27.7955	−	50.6858i	−0.988921	−	1.80332i
$791$		−	9.82172i		−	0.349220i
$792$	−1.85097	−	0.122302i	−0.0657714	−	0.00434582i
$793$		−	2.29543i		−	0.0815132i
$794$	−11.5582	+	6.33842i	−0.410187	+	0.224942i
$795$	0.0783599	−	0.0783599i	0.00277914	−	0.00277914i
$796$	−9.30420	+	14.5933i	−0.329779	+	0.517246i
$797$	−33.9793	−	33.9793i	−1.20361	−	1.20361i	−0.973061	−	0.230547i	$-0.925948\pi$
$797$	−33.9793	−	33.9793i	−1.20361	−	1.20361i	−0.230547	−	0.973061i	$-0.574052\pi$
$798$	−0.0308971	+	0.105934i	−0.00109375	+	0.00375001i
$799$	−41.5872			−1.47125
$800$	2.56152	+	16.7406i	0.0905634	+	0.591869i
$801$	34.6575			1.22456
$802$	−4.42796	+	15.1817i	−0.156357	+	0.536083i
$803$	1.49515	+	1.49515i	0.0527626	+	0.0527626i
$804$	−1.45929	+	2.28885i	−0.0514653	+	0.0807215i
$805$	9.01227	−	9.01227i	0.317641	−	0.317641i
$806$	−2.80862	+	1.54021i	−0.0989292	+	0.0542518i
$807$		−	2.24851i		−	0.0791512i
$808$	−1.63531	+	24.7495i	−0.0575301	+	0.870684i
$809$		−	31.2155i		−	1.09748i	−0.835994	−	0.548738i	$-0.815108\pi$
$809$		−	31.2155i		−	1.09748i	0.835994	−	0.548738i	$-0.184892\pi$
$810$	−16.6228	−	30.3121i	−0.584066	−	1.06506i
$811$	26.2088	−	26.2088i	0.920315	−	0.920315i	−0.0767367	−	0.997051i	$-0.524450\pi$
$811$	26.2088	−	26.2088i	0.920315	−	0.920315i	0.997051	+	0.0767367i	$0.0244501\pi$
$812$	9.30601	−	2.05965i	0.326577	−	0.0722796i
$813$	2.22358	+	2.22358i	0.0779845	+	0.0779845i
$814$	1.00839	+	0.294112i	0.0353441	+	0.0103086i
$815$	−21.9687			−0.769528
$816$	0.879945	−	2.41234i	0.0308043	−	0.0844487i
$817$	−3.96637			−0.138766
$818$	−2.67239	−	0.779442i	−0.0934380	−	0.0272526i
$819$	−1.42176	−	1.42176i	−0.0496804	−	0.0496804i
$820$	−7.08064	−	31.9921i	−0.247267	−	1.11721i
$821$	−33.9469	+	33.9469i	−1.18475	+	1.18475i	−0.206256	+	0.978498i	$0.566128\pi$
$821$	−33.9469	+	33.9469i	−1.18475	+	1.18475i	−0.978498	+	0.206256i	$0.933872\pi$
$822$	−1.04062	−	1.89759i	−0.0362957	−	0.0661861i
$823$		−	14.7754i		−	0.515039i	−0.966273	−	0.257520i	$-0.917095\pi$
$823$		−	14.7754i		−	0.515039i	0.966273	−	0.257520i	$-0.0829052\pi$
$824$	−7.71546	−	8.80719i	−0.268781	−	0.306813i
$825$			0.131813i			0.00458914i
$826$	−1.10865	+	0.607975i	−0.0385750	+	0.0211541i
$827$	−2.53233	+	2.53233i	−0.0880577	+	0.0880577i	−0.749764	−	0.661706i	$-0.769833\pi$
$827$	−2.53233	+	2.53233i	−0.0880577	+	0.0880577i	0.661706	+	0.749764i	$0.269833\pi$
$828$	−33.1377	−	21.1275i	−1.15162	−	0.734231i
$829$	23.4737	+	23.4737i	0.815276	+	0.815276i	0.985419	−	0.170143i	$-0.0544231\pi$
$829$	23.4737	+	23.4737i	0.815276	+	0.815276i	−0.170143	+	0.985419i	$0.554423\pi$
$830$	−6.77890	+	23.2421i	−0.235299	+	0.806745i
$831$	−1.90023			−0.0659181
$832$	6.35197	−	4.86338i	0.220215	−	0.168607i
$833$	21.1201			0.731768
$834$	1.23611	−	4.23811i	0.0428029	−	0.146754i
$835$	−8.05709	−	8.05709i	−0.278827	−	0.278827i
$836$	0.215956	+	0.137687i	0.00746901	+	0.00476199i
$837$	−1.89732	+	1.89732i	−0.0655809	+	0.0655809i
$838$	41.2473	−	22.6196i	1.42486	−	0.781381i
$839$			25.7184i			0.887897i	0.896052	+	0.443949i	$0.146423\pi$
$839$			25.7184i			0.887897i	−0.896052	+	0.443949i	$0.853577\pi$
$840$	0.711297	+	0.811945i	0.0245421	+	0.0280148i
$841$			20.2360i			0.697792i
$842$	12.1384	+	22.1346i	0.418316	+	0.762808i
$843$	0.427511	−	0.427511i	0.0147243	−	0.0147243i
$844$	−8.57571	−	38.7472i	−0.295188	−	1.33373i
$845$	1.99922	+	1.99922i	0.0687754	+	0.0687754i
$846$	−51.7498	−	15.0936i	−1.77919	−	0.518928i
$847$	7.43751			0.255556
$848$	−0.741080	−	0.270323i	−0.0254488	−	0.00928293i
$849$	−2.79036			−0.0957648
$850$	13.1283	+	3.82907i	0.450298	+	0.131336i
$851$	15.7358	+	15.7358i	0.539415	+	0.539415i
$852$	−6.00067	+	1.32810i	−0.205580	+	0.0454999i
$853$	27.2891	−	27.2891i	0.934362	−	0.934362i	−0.0636129	−	0.997975i	$-0.520262\pi$
$853$	27.2891	−	27.2891i	0.934362	−	0.934362i	0.997975	+	0.0636129i	$0.0202623\pi$
$854$	−1.06011	−	1.93314i	−0.0362763	−	0.0661506i
$855$			4.83850i			0.165473i
$856$	1.23329	−	18.6651i	0.0421530	−	0.637961i
$857$			47.0069i			1.60573i	0.596164	+	0.802863i	$0.296691\pi$
$857$			47.0069i			1.60573i	−0.596164	+	0.802863i	$0.703309\pi$
$858$	0.0545957	−	0.0299397i	0.00186387	−	0.00102212i
$859$	4.45046	−	4.45046i	0.151848	−	0.151848i	−0.627095	−	0.778943i	$-0.715756\pi$
$859$	4.45046	−	4.45046i	0.151848	−	0.151848i	0.778943	+	0.627095i	$0.215756\pi$
$860$	−20.8587	+	32.7162i	−0.711276	+	1.11561i
$861$	−0.553075	−	0.553075i	−0.0188487	−	0.0188487i
$862$	−7.71453	+	26.4500i	−0.262758	+	0.900890i
$863$	33.5477			1.14198			0.570989	−	0.820958i	$-0.306560\pi$
$863$	33.5477			1.14198			0.570989	+	0.820958i	$0.306560\pi$
$864$	3.96731	−	5.40073i	0.134970	−	0.183737i
$865$	−49.0418			−1.66747
$866$	10.0782	−	34.5541i	0.342471	−	1.17419i
$867$	0.922914	+	0.922914i	0.0313438	+	0.0313438i
$868$	−1.65400	+	2.59424i	−0.0561403	+	0.0880541i
$869$	−2.26469	+	2.26469i	−0.0768244	+	0.0768244i
$870$	−4.88923	+	2.68120i	−0.165760	+	0.0909012i
$871$			6.82896i			0.231390i
$872$	−2.07432	−	0.137060i	−0.0702452	−	0.00464142i
$873$		−	14.8059i		−	0.501104i
$874$	2.60901	+	4.75758i	0.0882510	+	0.160928i
$875$	2.72405	−	2.72405i	0.0920897	−	0.0920897i
$876$	−3.70434	+	0.819862i	−0.125158	+	0.0277006i
$877$	−13.7807	−	13.7807i	−0.465340	−	0.465340i	0.435061	−	0.900401i	$-0.356727\pi$
$877$	−13.7807	−	13.7807i	−0.465340	−	0.465340i	−0.900401	+	0.435061i	$0.856727\pi$
$878$	10.7882	+	3.14654i	0.364084	+	0.106191i
$879$	−3.62734			−0.122347
$880$	2.27138	−	1.05721i	0.0765683	−	0.0356387i
$881$	3.39279			0.114306			0.0571530	−	0.998365i	$-0.481798\pi$
$881$	3.39279			0.114306			0.0571530	+	0.998365i	$0.481798\pi$
$882$	26.2812	+	7.66529i	0.884934	+	0.258104i
$883$	21.5448	+	21.5448i	0.725041	+	0.725041i	0.969628	−	0.244586i	$-0.0786521\pi$
$883$	21.5448	+	21.5448i	0.725041	+	0.725041i	−0.244586	+	0.969628i	$0.578652\pi$
$884$	−1.39598	−	6.30736i	−0.0469517	−	0.212139i
$885$	0.523071	−	0.523071i	0.0175828	−	0.0175828i
$886$	−6.09675	−	11.1176i	−0.204824	−	0.373502i
$887$			52.6407i			1.76750i	0.467956	+	0.883752i	$0.344990\pi$
$887$			52.6407i			1.76750i	−0.467956	+	0.883752i	$0.655010\pi$
$888$	−1.41769	+	1.24195i	−0.0475744	+	0.0416772i
$889$		−	11.9300i		−	0.400119i
$890$	−41.0422	+	22.5071i	−1.37574	+	0.754440i
$891$	−1.35437	+	1.35437i	−0.0453732	+	0.0453732i
$892$	−27.9767	−	17.8370i	−0.936730	−	0.597227i
$893$	5.26273	+	5.26273i	0.176111	+	0.176111i
$894$	−1.66606	+	5.71224i	−0.0557213	+	0.191046i
$895$	−38.1638			−1.27568
$896$	3.10334	−	7.02934i	0.103675	−	0.234834i
$897$	1.31916			0.0440455
$898$	−13.2785	+	45.5266i	−0.443109	+	1.51924i
$899$	−11.2382	−	11.2382i	−0.374815	−	0.374815i
$900$	14.9468	+	9.52956i	0.498226	+	0.317652i
$901$	−0.450421	+	0.450421i	−0.0150057	+	0.0150057i
$902$	−1.59176	+	0.872904i	−0.0529998	+	0.0290645i
$903$			0.926196i			0.0308219i
$904$	30.7668	−	26.9530i	1.02329	−	0.896442i
$905$			45.9832i			1.52853i
$906$	−0.544854	−	0.993554i	−0.0181016	−	0.0330086i
$907$	−40.8915	+	40.8915i	−1.35778	+	1.35778i	−0.481135	+	0.876646i	$0.659775\pi$
$907$	−40.8915	+	40.8915i	−1.35778	+	1.35778i	−0.876646	+	0.481135i	$0.840225\pi$
$908$	10.2343	+	46.2411i	0.339638	+	1.53457i
$909$	18.3576	+	18.3576i	0.608885	+	0.608885i
$910$	2.60699	+	0.760368i	0.0864210	+	0.0252059i
$911$	48.7819			1.61622			0.808108	−	0.589034i	$-0.200491\pi$
$911$	48.7819			1.61622			0.808108	+	0.589034i	$0.200491\pi$
$912$	−0.416629	+	0.193920i	−0.0137959	+	0.00642132i
$913$	1.34137			0.0443928
$914$	38.5443	+	11.2420i	1.27493	+	0.371853i
$915$	0.912069	+	0.912069i	0.0301521	+	0.0301521i
$916$	−50.9999	+	11.2875i	−1.68508	+	0.372951i
$917$	−10.0403	+	10.0403i	−0.331561	+	0.331561i
$918$	−2.60194	−	4.74469i	−0.0858767	−	0.156598i
$919$		−	44.0850i		−	1.45423i	−0.686515	−	0.727115i	$-0.740861\pi$
$919$		−	44.0850i		−	1.45423i	0.686515	−	0.727115i	$-0.259139\pi$
$920$	52.9629	+	3.49950i	1.74613	+	0.115375i
$921$		−	4.36022i		−	0.143674i
$922$	−15.0755	+	8.26724i	−0.496485	+	0.272267i
$923$	−10.9330	+	10.9330i	−0.359863	+	0.359863i
$924$	0.0321515	−	0.0504284i	0.00105771	−	0.00165897i
$925$	−7.09763	−	7.09763i	−0.233369	−	0.233369i
$926$	14.8953	−	51.0700i	0.489491	−	1.67826i
$927$	−12.2555			−0.402523
$928$	31.9897	+	23.4992i	1.05011	+	0.771399i
$929$	−18.9640			−0.622189			−0.311094	−	0.950379i	$-0.600696\pi$
$929$	−18.9640			−0.622189			−0.311094	+	0.950379i	$0.600696\pi$
$930$	0.503987	−	1.72797i	0.0165264	−	0.0566622i
$931$	−2.67268	−	2.67268i	−0.0875937	−	0.0875937i
$932$	4.40325	−	6.90635i	0.144233	−	0.226225i
$933$	1.39585	−	1.39585i	0.0456981	−	0.0456981i
$934$	−16.0122	+	8.78094i	−0.523936	+	0.287321i
$935$		−	2.02308i		−	0.0661619i
$936$	0.552076	−	8.35534i	0.0180452	−	0.273103i
$937$			3.30552i			0.107987i	0.998541	+	0.0539933i	$0.0171950\pi$
$937$			3.30552i			0.107987i	−0.998541	+	0.0539933i	$0.982805\pi$
$938$	3.15385	+	5.75112i	0.102977	+	0.187781i
$939$	−1.05583	+	1.05583i	−0.0344556	+	0.0344556i
$940$	71.0852	−	15.7329i	2.31854	−	0.513151i
$941$	7.93569	+	7.93569i	0.258696	+	0.258696i	0.824524	−	0.565828i	$-0.191443\pi$
$941$	7.93569	+	7.93569i	0.258696	+	0.258696i	−0.565828	+	0.824524i	$0.691443\pi$
$942$	−0.437506	−	0.127605i	−0.0142547	−	0.00415759i
$943$	−38.4607			−1.25245
$944$	−4.94689	−	1.80447i	−0.161008	−	0.0587306i
$945$	2.27477			0.0739983
$946$	2.06370	+	0.601908i	0.0670966	+	0.0195697i
$947$	29.1091	+	29.1091i	0.945919	+	0.945919i	0.998611	−	0.0526914i	$-0.0167800\pi$
$947$	29.1091	+	29.1091i	0.945919	+	0.945919i	−0.0526914	+	0.998611i	$0.516780\pi$
$948$	−1.24184	−	5.61094i	−0.0403331	−	0.182235i
$949$	−6.74914	+	6.74914i	−0.219087	+	0.219087i
$950$	−1.17679	−	2.14591i	−0.0381803	−	0.0696225i
$951$		−	4.36815i		−	0.141647i
$952$	−4.08861	−	4.66714i	−0.132513	−	0.151263i
$953$			20.7344i			0.671652i	0.941924	+	0.335826i	$0.109015\pi$
$953$			20.7344i			0.671652i	−0.941924	+	0.335826i	$0.890985\pi$
$954$	−0.723964	+	0.397015i	−0.0234392	+	0.0128538i
$955$	25.9779	−	25.9779i	0.840625	−	0.840625i
$956$	36.7511	+	23.4312i	1.18862	+	0.757821i
$957$	0.218456	+	0.218456i	0.00706167	+	0.00706167i
$958$	10.5053	−	36.0185i	0.339412	−	1.16370i
$959$	−5.22946			−0.168868
$960$	−0.591480	+	4.45631i	−0.0190899	+	0.143827i
$961$	−25.8697			−0.834507
$962$	−1.32763	+	4.55191i	−0.0428045	+	0.146759i
$963$	−13.8446	−	13.8446i	−0.446138	−	0.446138i
$964$	−9.07256	−	5.78436i	−0.292208	−	0.186302i
$965$	−23.7771	+	23.7771i	−0.765411	+	0.765411i
$966$	1.11095	−	0.609235i	0.0357443	−	0.0196018i
$967$			1.15830i			0.0372485i	0.999827	+	0.0186243i	$0.00592863\pi$
$967$			1.15830i			0.0372485i	−0.999827	+	0.0186243i	$0.994071\pi$
$968$	20.4102	+	23.2982i	0.656008	+	0.748833i
$969$			0.371085i			0.0119210i
$970$	9.61516	+	17.5334i	0.308724	+	0.562965i
$971$	17.9235	−	17.9235i	0.575192	−	0.575192i	−0.358383	−	0.933575i	$-0.616672\pi$
$971$	17.9235	−	17.9235i	0.575192	−	0.575192i	0.933575	+	0.358383i	$0.116672\pi$
$972$	−2.27863	−	10.2954i	−0.0730871	−	0.330226i
$973$	−7.54304	−	7.54304i	−0.241819	−	0.241819i
$974$	−12.1118	−	3.53259i	−0.388088	−	0.113191i
$975$	−0.595008			−0.0190555
$976$	3.14642	−	8.62579i	0.100714	−	0.276105i
$977$	41.7610			1.33605			0.668026	−	0.744138i	$-0.267139\pi$
$977$	41.7610			1.33605			0.668026	+	0.744138i	$0.267139\pi$
$978$	−2.09660	−	0.611503i	−0.0670418	−	0.0195537i
$979$	1.83381	+	1.83381i	0.0586087	+	0.0586087i
$980$	−36.1007	+	7.98997i	−1.15319	+	0.255230i
$981$	−1.53860	+	1.53860i	−0.0491237	+	0.0491237i
$982$	−26.4211	−	48.1794i	−0.843130	−	1.53747i
$983$			21.1333i			0.674047i	0.941496	+	0.337023i	$0.109420\pi$
$983$			21.1333i			0.674047i	−0.941496	+	0.337023i	$0.890580\pi$
$984$	0.214761	−	3.25028i	0.00684633	−	0.103615i
$985$			40.0785i			1.27701i
$986$	28.1038	−	15.4118i	0.895007	−	0.490812i
$987$	1.22891	−	1.22891i	0.0391167	−	0.0391167i
$988$	−0.621521	+	0.974834i	−0.0197732	+	0.0310136i
$989$	32.2037	+	32.2037i	1.02402	+	1.02402i
$990$	0.734255	−	2.51746i	0.0233362	−	0.0800102i
$991$	45.4743			1.44454			0.722269	−	0.691612i	$-0.243099\pi$
$991$	45.4743			1.44454			0.722269	+	0.691612i	$0.243099\pi$
$992$	−12.6654	+	1.93797i	−0.402128	+	0.0615307i
$993$	4.03967			0.128195
$994$	−4.15815	+	14.2566i	−0.131889	+	0.452192i
$995$	−17.3003	−	17.3003i	−0.548456	−	0.548456i
$996$	−1.29390	+	2.02944i	−0.0409988	+	0.0643052i
$997$	−15.4587	+	15.4587i	−0.489583	+	0.489583i	−0.908175	−	0.418592i	$-0.862524\pi$
$997$	−15.4587	+	15.4587i	−0.489583	+	0.489583i	0.418592	+	0.908175i	$0.362524\pi$
$998$	52.8631	−	28.9896i	1.67335	−	0.917649i
$999$			3.97183i			0.125663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.2.n.a.157.10	yes	48
4.3	odd	2		832.2.n.a.209.12		48
8.3	odd	2		1664.2.n.a.417.13		48
8.5	even	2		1664.2.n.b.417.12		48
16.3	odd	4		1664.2.n.a.1249.13		48
16.5	even	4	inner	208.2.n.a.53.10	✓	48
16.11	odd	4		832.2.n.a.625.12		48
16.13	even	4		1664.2.n.b.1249.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
208.2.n.a.53.10	✓	48	16.5	even	4	inner
208.2.n.a.157.10	yes	48	1.1	even	1	trivial
832.2.n.a.209.12		48	4.3	odd	2
832.2.n.a.625.12		48	16.11	odd	4
1664.2.n.a.417.13		48	8.3	odd	2
1664.2.n.a.1249.13		48	16.3	odd	4
1664.2.n.b.417.12		48	8.5	even	2
1664.2.n.b.1249.12		48	16.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.395977 + 1.35765i) q^{2} +(-0.140536 - 0.140536i) q^{3} +(-1.68640 - 1.07519i) q^{4} +(1.99922 - 1.99922i) q^{5} +(0.246447 - 0.135149i) q^{6} -0.679168i q^{7} +(2.12751 - 1.86379i) q^{8} -2.96050i q^{9} +O(q^{10})\)	\(q+(-0.395977 + 1.35765i) q^{2} +(-0.140536 - 0.140536i) q^{3} +(-1.68640 - 1.07519i) q^{4} +(1.99922 - 1.99922i) q^{5} +(0.246447 - 0.135149i) q^{6} -0.679168i q^{7} +(2.12751 - 1.86379i) q^{8} -2.96050i q^{9} +(1.92259 + 3.50588i) q^{10} +(0.156646 - 0.156646i) q^{11} +(0.0858968 + 0.388103i) q^{12} +(0.707107 + 0.707107i) q^{13} +(0.922069 + 0.268935i) q^{14} -0.561924 q^{15} +(1.68792 + 3.62642i) q^{16} +3.23000 q^{17} +(4.01931 + 1.17229i) q^{18} +(-0.408747 - 0.408747i) q^{19} +(-5.52105 + 1.22195i) q^{20} +(-0.0954473 + 0.0954473i) q^{21} +(0.150642 + 0.274699i) q^{22} +6.63737i q^{23} +(-0.560919 - 0.0370625i) q^{24} -2.99379i q^{25} +(-1.24000 + 0.680002i) q^{26} +(-0.837663 + 0.837663i) q^{27} +(-0.730237 + 1.14535i) q^{28} +(-4.96165 - 4.96165i) q^{29} +(0.222509 - 0.762894i) q^{30} +2.26501 q^{31} +(-5.59177 + 0.855612i) q^{32} -0.0440288 q^{33} +(-1.27901 + 4.38519i) q^{34} +(-1.35781 - 1.35781i) q^{35} +(-3.18311 + 4.99260i) q^{36} +(2.37078 - 2.37078i) q^{37} +(0.716788 - 0.393079i) q^{38} -0.198747i q^{39} +(0.527242 - 7.97949i) q^{40} +5.79456i q^{41} +(-0.0917886 - 0.167379i) q^{42} +(4.85187 - 4.85187i) q^{43} +(-0.432594 + 0.0957439i) q^{44} +(-5.91870 - 5.91870i) q^{45} +(-9.01120 - 2.62825i) q^{46} -12.8753 q^{47} +(0.272429 - 0.746854i) q^{48} +6.53873 q^{49} +(4.06450 + 1.18547i) q^{50} +(-0.453930 - 0.453930i) q^{51} +(-0.432191 - 1.95274i) q^{52} +(-0.139449 + 0.139449i) q^{53} +(-0.805554 - 1.46894i) q^{54} -0.626342i q^{55} +(-1.26582 - 1.44494i) q^{56} +0.114887i q^{57} +(8.70087 - 4.77146i) q^{58} +(-0.930857 + 0.930857i) q^{59} +(0.947631 + 0.604177i) q^{60} +(-1.62312 - 1.62312i) q^{61} +(-0.896894 + 3.07509i) q^{62} -2.01068 q^{63} +(1.05260 - 7.93045i) q^{64} +2.82733 q^{65} +(0.0174344 - 0.0597755i) q^{66} +(4.82880 + 4.82880i) q^{67} +(-5.44708 - 3.47287i) q^{68} +(0.932787 - 0.932787i) q^{69} +(2.38108 - 1.30576i) q^{70} +15.4616i q^{71} +(-5.51774 - 6.29849i) q^{72} +9.54473i q^{73} +(2.27991 + 4.15746i) q^{74} +(-0.420734 + 0.420734i) q^{75} +(0.249830 + 1.12879i) q^{76} +(-0.106389 - 0.106389i) q^{77} +(0.269829 + 0.0786995i) q^{78} -14.4573 q^{79} +(10.6246 + 3.87551i) q^{80} -8.64606 q^{81} +(-7.86696 - 2.29452i) q^{82} +(4.28152 + 4.28152i) q^{83} +(0.263587 - 0.0583383i) q^{84} +(6.45749 - 6.45749i) q^{85} +(4.66589 + 8.50836i) q^{86} +1.39458i q^{87} +(0.0413113 - 0.625222i) q^{88} +11.7067i q^{89} +(10.3792 - 5.69183i) q^{90} +(0.480244 - 0.480244i) q^{91} +(7.13646 - 11.1933i) q^{92} +(-0.318315 - 0.318315i) q^{93} +(5.09833 - 17.4801i) q^{94} -1.63435 q^{95} +(0.906087 + 0.665599i) q^{96} +5.00115 q^{97} +(-2.58919 + 8.87728i) q^{98} +(-0.463752 - 0.463752i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4} - 12 q^{8}+O(q^{10}) \) 48 * q - 4 * q^4 - 12 * q^8	\( 48 q - 4 q^{4} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 8 q^{12} - 4 q^{14} - 16 q^{15} + 12 q^{16} - 16 q^{19} - 28 q^{20} + 12 q^{22} + 28 q^{24} - 16 q^{29} + 4 q^{30} + 24 q^{31} - 20 q^{32} - 40 q^{34} + 24 q^{35} + 8 q^{36} - 16 q^{37} + 32 q^{40} + 40 q^{42} - 8 q^{43} + 20 q^{44} - 32 q^{46} - 40 q^{47} - 52 q^{48} - 48 q^{49} - 16 q^{50} - 24 q^{51} - 8 q^{52} + 16 q^{53} + 20 q^{54} + 20 q^{56} - 16 q^{58} - 68 q^{60} + 32 q^{61} - 32 q^{62} + 40 q^{63} + 32 q^{64} - 32 q^{66} + 16 q^{67} + 40 q^{68} + 32 q^{69} - 60 q^{70} + 40 q^{72} + 72 q^{74} - 40 q^{75} - 28 q^{76} + 16 q^{77} + 32 q^{79} - 52 q^{80} - 48 q^{81} + 40 q^{82} + 40 q^{83} - 36 q^{84} - 32 q^{85} - 72 q^{86} - 8 q^{88} + 28 q^{90} + 36 q^{92} + 28 q^{94} - 48 q^{95} + 68 q^{96} + 64 q^{98} - 40 q^{99}+O(q^{100}) \) 48 * q - 4 * q^4 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 8 * q^12 - 4 * q^14 - 16 * q^15 + 12 * q^16 - 16 * q^19 - 28 * q^20 + 12 * q^22 + 28 * q^24 - 16 * q^29 + 4 * q^30 + 24 * q^31 - 20 * q^32 - 40 * q^34 + 24 * q^35 + 8 * q^36 - 16 * q^37 + 32 * q^40 + 40 * q^42 - 8 * q^43 + 20 * q^44 - 32 * q^46 - 40 * q^47 - 52 * q^48 - 48 * q^49 - 16 * q^50 - 24 * q^51 - 8 * q^52 + 16 * q^53 + 20 * q^54 + 20 * q^56 - 16 * q^58 - 68 * q^60 + 32 * q^61 - 32 * q^62 + 40 * q^63 + 32 * q^64 - 32 * q^66 + 16 * q^67 + 40 * q^68 + 32 * q^69 - 60 * q^70 + 40 * q^72 + 72 * q^74 - 40 * q^75 - 28 * q^76 + 16 * q^77 + 32 * q^79 - 52 * q^80 - 48 * q^81 + 40 * q^82 + 40 * q^83 - 36 * q^84 - 32 * q^85 - 72 * q^86 - 8 * q^88 + 28 * q^90 + 36 * q^92 + 28 * q^94 - 48 * q^95 + 68 * q^96 + 64 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more